"I have 2 children, one of which is a girl" "So is the other one a boy?" "No, the other one's a girl too." "Then why didn't you just say that?" "Alright, I have 2 girls, one of which is a girl."
The change of probability from 1/3 to 50% is, in fact, based off the fact that the focus of the analysis has moved, with the introduction of new information (the name) which pertains to a population (daughters) which differs from the starting one (families). To exemplify this, I'd draw your attention to 2:15. This question can be easily rephrased to give 50% as a correct answer. Let's look at the information you provide in terms of children, rather than families. With 1,000 families with 2 children each, we have a total of 2,000 children. These can be represented as follows: [notation: (X|Y) means persons of gender X given their sibling is of gender Y] 500(B|B) [or 250(B,B) pairs]; 500(B|G); 500(G|B) [or 500(B/G,G/B) pairs]; 500(G|G) [or 250(G,G) pairs]. If I now asked "what is the probability of this girl's sibling being a sister?" the answer would be 50%. In actual fact, we'd have 500 girls with sisters, over a population of 500+500 = 1,000 girls. Both answers are correct: 1/3 of families with a daughter have two, and 50% of girls have a sister. Looking at the problem at hand, the issue is that the information "1% of people named 'Julie'" (note: the issue is not the name, but its assumed distribution) is disproportionately applied to the girls population - ie, 1% of (B,G/G,B) and 2% of (G,G) are taken. What you are therefore answering is "what is the probability of this girl named 'Julie' having a sister?". The answer remains unsurprisingly 50% as above. It is therefore incorrect, in my opinion, to disproportionately apply this to the siblings pairs, in that you are moving your focus from the families to the girls. To see this, we can change the problem slightly: if the assumption drawn from the name was that "1% of *all families with a daughter* name their daughter 'Julie'", you'd end up with your probability of 1/3 - as before. We take our 10,000 families. 5,000 are (B,G/G,B) pairs; 2,500 are (G,G) pairs. 1% of all families name their children 'Julie', so 50(B,G/G,B) pairs would have a person named Julie in them and 25(G,G). 25/75 = 1/3 as before.
Stipulating that 1% of all families with a daughter name their daughter Julie does not change the way in which we might expect the names to be distributed. If one family has two girls, and thus two opportunities to name a child Julie, then we would typically expect that two-girl families are twice as likely to have a child named Julie than families with only one girl.
@@James-rq9qb Ah, but you see, with your assumption you're providing additional data on the distribution of the name Julie. Up to that point I know that the family have a daughter, whose name is X, where X has an unknown distribution. When I'm told that X = 'Julie', 'Julie' still has an unknown distribution until I observe that this is not the case - and I'm told nothing in this regard - making the information effectively useless. The distribution does not follow from receiving the name. It follows from looking at a population sample and take very meaningful measurements, which do affect your probability space (ie, you're literally counting how many families with a daughter have a 'Julie' in them and how many families with two daughters have a 'Julie' in them). When you say that families with two daughters are twice as likely to name their daughter 'Julie', you're describing a behaviour that, albeit of common sense, does not mathematically follow from anything you've been told. You're therefore introducing new information in your analysis through a behavioural bias. Say, for example, that the daughter was named 'Alex'. As this is a gender-neutral name, I could make no educated guesses as to how this would affect my analysis. However, I could go in the population of families with at least a daughter and two daughters, and measure how many had an 'Alex' in them, adjusting my final conclusions.
You are not fully correct. The disproportionate chances of "Julie" appearing in (BG,GB) and (GG) pairs is only part of why this happens. It becomes more clear, what changes if you give a direct mathematical formulation: Let X1 and X2 be two identically distributed but not independent random variables. Let P1 be a predicate such that P1(X1) is true with chance 1/2 and likewise P1(X2) is true with chance 1/2 (the gender). Also, let P1(X1) and P1(X2) be independent. The statement that leads to 1/3 chance is: Given that P1(X1) OR P1(X2) ("one of them is a girl") is true, what is the chance that P1(X1) AND P1(X2) ("both are girls") is true. Now for the "Julie" case: Let P2 be a predicate, such that P2(X1) AND P2(X2) must be false (can be ensured by X1 and X2 not being independent). Also, let there be a non-zero chance that P2(X1) is true and a non-zero chance that P2(X2) is true (those are the 1% of Julies in the population). Given that (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), what is the chance that P1(X1) AND P1(X2) are true? The answer is 1/2 because the chance of P2(X1) AND P2(X2) is zero. Now the "Tuesday" case: Let P2 be a predicate, such that P2(X1) is true with chance 1/7 and likewise for P2(X2) with P2(X1) and P2(X2) being independent. Given that (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), what is the chance that P1(X1) AND P1(X2) are true? The answer is 13/27 because the chance of P2(X1) AND P2(X2) is 1/49 and therefore larger than zero. Here one more obviously sees the differences between the Julie case and the other cases. It all depends on the probability of P2(X1) AND P2(X2) being true (zero in the Julie case, non-zero in other cases). In fact, I believe it should be possible to factor out this term somewhere from (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), but I cannot quite get this to work currently. Also, by setting the probability of P2(X1) AND P2(X2) to arbitrary values, one should be able to get any probability between 1/3 and 1/2 (although I cannot proove this directly). Imagine a scenario "I have a child, one of them is a girl who has this hereditary disease that co-occurs in siblings with a chance of p". Then this would further change the probability of P1(X1) AND P1(X2). In the case where you get 1/3 chances with the girl naming Julie, you are changing another aspect of the puzzle. Now you are modifying the probability of P2(X1) OR P2(X2) (meaning the total chance that a family names one of their children Julie). Because this term also appears when factoring (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), it changes the probability back to 1/3, although P2(X1) AND P2(X2) still is zero in this case.
The enunciation needs to be a bit clearer, but I see where this could be going. we'd have to start with the event of both kids being born at the same time. which is funny... really... because it seems like nobody actually has a damn clue about that... or none that I could find. that will be the basis of our probability distribution. we will say we have a probability W1 for not twins and W2 for twins ( and of course, they add up to 100% ) for the W2 case, it's a 25% of having 2 girls, so overall that is W2 / 4 in our situation for the other one tho... we will suppose that if they are not twins, the other kid was not born in a boat, so it bares a Julia case distribution... therefore W1/2 Case solved (ish ) Ok, ok... the chance of having fraternal twins... is 1/125 ( suggests a source on a math forum, take this with a grain of salt ) in that case, we have a chance of 62/125 + .25 / 125 which adds up to 62.25 / 125 god save us all 0.498 yaay...
Wow, that's almost exactly what I said to myself when he paused just after 10:57 ! For some reason I chose "lifeboat" for what I thought he was going to say. Although, I think this shows why the probability doesn't change until they quantify that new piece of information. Not for watercraft, because apparently that's common enough that we both jumped to it, but if they were to say "leap day" then we really know the probability would be lower.
If someone tells you they "have two children, one of whom is a girl named Julie", you can't really make the assumption that they're not weird enough to name both their daughters Julie.
If all girls were called either Julie or Zoe, evenly distributed and with no same names, 100% of the 33% would have a Julie but 50% of the 66% would have a Julie. That's a better explanation I think
@@carllorenzandonaque9242 Nitpick #1: It matters how common the name "Julie" is. If we make the same illogical assumption that lead to the 1/3 answer - that you can't know "I have two children, and at least one is a boy" for any family that has a boy and a girl? Then the answer is (2-J)/(4-J), where J is the frequency with which girls are named "Julie." This is the answer that Leonard Mlodinow gets, but I don't think he put it in "The Drunkard's Walk." He just said "close to 1/2." But he has said it on forums. Note that if J=1, this is 1/3, the answer he got without the name. And as J approaches 0, it approaches 1/2. Nitpick #2: The assumption that you can't have two Julies in the same family also means that you can't have two Marys, two Anns, two Constances, or two Sunshine Angels. That really throws a wrench in the calculation. And it turns out that if the name is rare - as Mlodinow did, he used "Florida" - the chances of another girl are actually greater than 1/2, not less. This is because the rule affects very few families, so a two-girl family is essentially twice as likely to have two "Floridas" as a one-girl family. But the high chances that a first girl has a common name like Mary reduces that. The answer is close to (1+A-J)/(3+A-J), where A is the frequency of the average name.
here's a way to rephrase the questions that makes intuitive sense: the first question is "given that I have 2 children, at least one of which is a girl, what is the probability that they are both girls?" the second question is "I have a daughter. What is the probability that her sibling is a girl?" the first question is conditional probability in the second question, despite the fact that you can mince words to make the questions virtually identical, you are only asking about the probability of one specific person's gender
@@darbyl3872 I flipped two coins, one of them came out Heads. This gives you 4 scenarios (HH, TH, HT, TT) There are 3 scenarios that have one H and of those 3 you have 1 of them being double H. (So you have 1/3 - 33% - The first question) I flip a coin. It's Heads. I flip a second coin. What is the probability of it being Heads? (Since you don't care about the first coin anymore you just have to guess what the second is - 50% - the second question)
Professional statistician here: I can explain this. The issue is that the math in this video is subtly wrong. Here is why: You have to be really careful about probability, and particularly about conditional probability when you suddenly introduce new information: What does this do to your probability distribution and what does it do to your sample space? There are actually two situations here, and they are actually different. 1) You ask a guy: "Do you have a daughter?" He says "yes". You then ask "What is her name?" and he says "Julie". 2) You ask a guy: "Do you have a daughter?" He says "yes." You then ask "Do you have a daughter named Julie?" And he says "ZOMG you are a wizard! Yes I do!" In the first case, the probability of him having a second daughter is still 33% as before, and in the second it is 50%. This can be thought of as follows: In the first case, if the guy has one daughter named Julie he will name her, but if he has two daughters he might name Julie, but he might also NOT name Julie and may name the other one instead. This means that if he has a daughter named Julie, he might not always tell you this. In fact, he will only tell you so 50% of the time, which reduces exactly to the case when you don't know her name: Most of the time he will only have one daughter. In the second case, the probability of him having a second daughter is 50%, and this is also somewhat intuitive. You just did a pretty shocking bit of guesswork with her name, but your guess would have had a better chance of success if he had two daughters than only one, right? The same thing works for Tuesday, pretty much exactly the same way as in the name situation. For physical presence it is slightly different, but the reason is still somewhat similar. The "there she is", might be enough to get the 50% answer form the video. We have to understand the distribution of people who are there. For instance, imagine you are sitting there and there are two kids, a boy and a girl, and he points to the girl and says "there she is". Do you still think there is a 50% chance the other is a girl? How about if there are two girls there and he points to one of them? How about if there is only one other person in the room and it happens to be his daughter? Note that these situations are all different from each other. EDIT: OK I just saw that this was addressed in another video by the same guy. I still want to leave the answer up though, just in case someone does not find the other video.
tuerda I’m a graduate student in statistics. Another issue I have was the subtle assertion that if one daughter is named Julie, the chance of the other being named Julie is zero. This reduces the sample space entirely to a conditional sample space on the other daughter. This changes what was previously a combination to a permutation, where only one spot in the permutation is unknown. This is the chance that one kid is a girl, 50%.
You don't get the core of the problem which is that probability theory doesn't apply for these examples. Which is funny given that you claim to have a profession in a related field. Obviously that profession prevents you from seeing clearly. The question the video asks is not a probability question. You need a repeated experiment to claim any probability. The probability is determined in the construction of the experiment. None of you (you and the video maker) have described any actual repeated experiment, so there is no answer here.
@@StefanReich The meaning of "probability" is a messy philosophical question. An extremely frequentist stance does require repeated experimentation, but this is not the only interpretation (nor, for that matter, even the most popular one anymore). The wikipedia article on "probability interpretations" reasonably sums up the complete chaos involved arguing about what probability is. I can elaborate or give you further references if you like, but this rabbit hole is **deep**.
What if I have two kids, one that is a girl named George, was born on a leap day February 29th, does not like ponies and only regularly keeps a diary and rather eats corn flakes than rice crispies? I think we can all agree that chances of my other kid being a boy is infinitesimal at best. Nearly 100% probability the other child is hermaphrodite, lift up the scrotum and there's a big ugly cooch behind.
I feel this is approached from a strange angle - the idea that the probability is based on if the older sibling is the girl mentioned or not. The question is simply "What is the probability of the other child being a boy or girl?" then it truly is 50/50, since there are only two, equally probably outcomes. The paradox in the video only comes into question because they're assuming that A) In the pool of numbers the probability stems from that there is an equal number of boy/boy, boy/girl and girl/girl options but that there are also additional options of which one is the older/younger sibling. B) That the older sibling/younger sibling pairing counts as a separate pool to draw probability numbers from, even though that factor is entirely irrelevant to the initial question. If the question was "What is the probability of the other child being a girl and the younger/older sibling" then the probability would shift.
No, but the fact that boy/girl families are twice as common as girl/girl families is very relevant. Showing that through the older/younger chart was an easy way to help people wrap their heads around the concept, but your right, age doesn't matter. The math still checks out, though. An easy way to check this is two flip two coins, over and over again. You'll find that about half the time you get one head and one tail, but only a quarter of the time will you get two heads, making the mixed tosses twice as likely as the matched toss you're looking for.
Edit: Made a follow up video with an explanation saying mostly the same things I say in the paragraphs below - th-cam.com/video/ElB350w8iJo/w-d-xo.html Okay if you haven't watched the video yet (and have never seen this paradox), then don't read the following paragraphs just yet. Look at the math I show and see what conclusions you can come to. After A LOT of thought I see some issues but they are very subtle and not obvious....well they weren't to me, but I want to try and clear everything up below. TLDR: The fact some GG parents who have a daughter named Julie won't tell you about Julie but rather the other daughter matters here. So if we only know that the people in some room have 2 kids, then when one tells us they have a daughter, the probability is 50%, when they mention the name, it stays 50%. If instead we know everyone has 2 kids and at least one daughter (this is known before talking to anyone) then the probabilities all are 33.3%. Longer Version: So first I think all the math in this video holds and is perfectly accurate IF we treat this more like a typical probability problem and phrase it like this. "If we have a room full of people who have two children then ask those with at least one daughter to step forward, what is the probability a randomly selected one has 2 daughters?" This answer is 33.3% as stated in the video. If you then ask all of those people who have a daughter named Julie to step forward then 50% of those families will have 2 daughters, also as stated in the video (because you have twice as many potential Julie's in each (girl, girl) family). And lastly if instead of the name we ask those with a daughter who was born on a Tuesday to step forward, then 13/27 of those will have two daughters. All of that is correct and although it may seem kind of weird, I wouldn't call those paradoxes. However, in any stats class when we are GIVEN something, we rarely think about HOW we are given that information and in this problem we need to. Imagine a room of 7500 fathers who have 2 children, one of which is a girl (that means 5000 will have a son and daughter, while 2500 of them have 2 daughters). Then let's say you talk to every single father in that room and at some point in conversation they all end up randomly mentioning the name of one of their daughters (or their only daughter if it's a GB/BG family). If 1/100 girls are named Julie, then 500 fathers with a son and daughter will have told you Julie (which is every BG/GB father in that room who has a daughter named Julie as there's no other daughter for them to name). Then of the GG families there WILL be 500 fathers with a daughter named Julie as I stated in the video, assuming no overlap. However, only half of them will tell you of Julie, the other half will tell you of their other daughter. That means you've heard the name Julie from 250 GG fathers that night and 500 GB/BG families. If every single time you heard the name Julie you bet $1 they have 2 daughters, you'd win $250 but lose $500 and thus end at a loss. You'd only win 33.3% of the time which keeps the same probability as BEFORE we heard the name. This here kind of resolves the paradox I mentioned in the video with the whole "i have a daughter....whose name is Julie" part. The thing to note is that some of those GG fathers with a daughter named Julie will not tell you about her but rather the other daughter. So you're not HEARING about Julie from the GG families enough for it to be 50% and this reflects reality more of talking to someone in a bar who states the name of their daughter. And actually you could argue there's a flaw in the previous paragraph because of HOW we obtain the fact that the father has at least one daughter. Imagine we are in a room full of 1000 fathers that have 2 kids but we DON'T know they all have at least one daughter (250BB, 500GB/BG, and 250GG). We then talk to all of them and throughout the conversation they all mention the gender of one of their children at random. That leaves 250 fathers with a boy and girl (half of the total) that told you they have a daughter and 250 fathers with two daughters (all of them) who said the same thing (since that was the only option for them). Because of this you have a 50% chance of guessing correctly that they have 2 daughters. If those fathers then tell you the name of one of their daughters and you analyze all who say Julie (or any name for that matter) you retain that 50% probability. To summarize, it's all about whether you know something about all the parents in that room vs what they tell you at random during conversation. When you to a bar full of strangers, since you don't know anything about the people there in terms of how many kids they have, you could say the 50% stays consistent in this video. But if we know the parents in that room have 2 kids, one is a girl, you get the 33.3% in every situation. And if you know everyone in that room also has a daughter named Julie, then you go to the 50%.
Agreed. Just one small caveat regarding the last sentence. It's not just that you know that everyone in the room has a daughter names Julie that enables you to say that the other sibling is a girl with 50% probability. It's rather the fact that they have been selected from a random population of two-children families (with randomly assigned genders) on the basis of the selection criterion that one sibling is named Julie. If you had rather selected them on the condition that the younger sibling is named Julie, then you would still know that everyone in the room has a daughter named Julie but, in that case, the probability that the other sibling is a girl would be 1/3.
...and that's because, in the later scenario, we would have effectively discarded from the population under consideration all the families in which it's the older older sibling who is named Julie.
I'm going as far as to say that the math presented in the video is plainly wrong, because you're mixing up implicit assumptions that are never mentioned. The mathematical analysis you have made in the extra pinned comment is completely correct and essential for understanding this seemingly 'paradox', but the main video suggest something completely different that is just incorrect and probably very confusing for many viewers. In the video, you act as if just hearing the parent in the bar say the name Julie changes the probability from 33% to 50%. This is NOT the case. As you explain in the pinned comment, the probability only changes if you ask all parents with a child named Julie to step forward. In this way, you are sure that 100% of the parents with two daughters, one of which is called Julie, step forward. However, if the parent in the bar just gives you a random name of a daughter, only in 50% of the cases of a parent with two daughters, one of which is called Julie, they will say the name Julie and 50% of the time the other name. You can do your whole analysis again and see that the probability is still 33%. In the same way, one can see that in all cases in the video where you claim that a probability 'suddenly and counterintuitively' changes when we get extra information, this is not really the case in the setup in which you explain the paradox. The main reason the story sounds paradoxical is because it is WRONG, not because it is complicated. I hope you could emphasize more in the first line of the video description that probability theory is not actually so paradoxical as you describe it to be. I would highly appreciate it if you coud include something like "WARNING: this video is made under a wrong conception of the paradox and the math behind it. Please read the pinned comment for the correct mathematical analysis." It would be a shame if after this video people think they have learnt something about how probabilities work, but what they have learnt is actually false. Thanks in advance!
@@bastiaanabcde I agree that the video is misleading, but I am also impressed how very fast after posting it MajorPrep rethought the problem completely through and arrived at a correct conception. That's not something that you see very often on the Internet. I am fairly sure he's going to either make a followup video or edit in some caveat in the way you are suggesting.
@@pokerandphilosophy8328 Yes, I was also very happy to see this mathematical analysis, and indeed for internet standards this is surprisingly correct. So well done MajorPrep! Now let's make sure the viewers actually get aware of this haha.
In your first point at 1:20 when claiming that there is a 33% chance of the other sibling being a girl, there is a really big problem with how you are presenting the case. When comparing the known girl to the the potential boy, you state the possibilities as *girl born first - boy born second* or *boy born first - girl born second.* But when comparing the known girl to the potential girl, you just say "and two girls." But in the case of a comparison of the known girl with the potential girl, one of them still must be born first and the other must be born second, and there are two equally likely orders in which this can happen, giving this scenario two outcomes to compare against the two outcomes of the boy-girl/girl-boy pairs. The problem arises because you are selectively identifying the known girl. When comparing her to the potential boy, you give her the identity of "older/first" or "younger/second," aka order-of-birth. However, you fail to preserve that order-of-birth identity when comparing the known girl to the potential girl. If you were consistent in the way you analyze the outcomes, you would see that the probability is *always* a 50% chance of the other child being a girl because the known girl would still have to be "older/first" or "younger/second". You can see this in your second argument when you use a name as an identifier rather than order-of-birth. By not remaining consistent in the first argument, you're ruining the integrity of the comparison.
this problem somehow reminds me of the 3 doors thing where there is a game and there are 3 doors and you choose one the game master opens a door that would be a fail and then you can change your mind to the other door or keep your first choice and you should always change the choice cause the first time picking it was 2/3 chance to fail and now it would be more probably to change or something like that
I think the intuitiveness comes more readily when you just think of it as "the math changes when you are liking at it from the perspective of the identified daughter", whether it be that she's identified by her name, day she was born, etc.
I wish it was, but frankly, I had an exam with harder shit than this... yeah, it's weird, but probabilities get a lot weirder still, with pretty... complicated stuff that one would not even dare use intuition for, simply because most of the time you need 10 hours to understand the problem anyway...
actually it is not... math is a very precise thing, even those bits that seem random, like rolling a die. it is a condition that just one girl is named Julia. if both kids could have the same name... well.. the probability of both kids being girls would be 3/5
this reminds me of how in quantum physics, once you make a meassurement it collapses the wave function, just like labeling a girl a certain way changes the probability
Man: I have 2 children one of wich is a girl born on a Tuesday, her name is julie, she's standing next to me, is left handed and wears glasses. What is the probability of that family having a dog?
The ambiguity here is easier to spot if you reformulate this as questions and answers. Q: Do you have at least one daughter? A: Yes, and incidentally the name of the daughter I am thinking of is Julie Then the probability is 1/3 Q: Do you have a daughter named Julie? A: Yes Then the probability is 1/2
yes exactly. There is only a "paradox" because the problem is formulated in an ambiguous way. If you would ask everyone "Do you have at least one daughter, give me a name of one daughter and they answer: "I have at least one daughter, her name is Julie". The probability is *drumroll* still 1/3. A simple symmetry argument suffices. But what may confuse some people is that they forget the fact, that only 1/2 of those that have two daughters, one named Julie, will actually give you the name Julie. 1/2 of the people that have exactly two daughters, will tell you the name of the other daughter
The name doesn't actually make it 50 50 in that scenario. There'd be some overlap. Or chance of overlap. I'm not sure the math. But let's say we now have 50 b/g families with a Julie. And 50 b/g families with a Sarah. However there'd be 98 or 99 families with a Sarah and a Julie. Even if it's 99.9 families. It's still overlap. This is the same logic as his birthday Tuesday math
@@qwertz12345654321 The question posed by the video has the parent stating that she has at least one daughter, so theoretically, in the GB/BG cases there's a 1/2 chance of saying she has at least one son. Does that mean there is a difference between you asking if someone has a daughter, and them simply stating it? I would say yes, because if you ask all 2-child parents if they have a daughter, 75% will answer 'yes', but if you ask them all to state the gender of one of their children, only 50% will answer 'girl'.
@@MatthewJensen77 yes definitely. It is very important to closely observe the information you are given, which doesn't always have a intuitive interpretaton.
Oh I understand now! Adding the name is switching the question from "If I have 2 kids and one is a girl, what are the odds of the other being a girl?" to "Given I have 2 kids, and I have a girl X, what are the odds of X's sibling being a girl?"
The problem with this is cherry picking the distinction between the girls. He's deciding that when you dont have an identifier (g1, g2) is the same as (g2, g1) which in statistics is already incredibly wrong. Even without given identifiers you must always count both versions of two girls as separate, distinct, and plausible outcomes.
But (and correct me if I'm wrong) if we take in account the birth position (boy first born or second born) to split the B/G probability, then we should double the G/G too. That girl might be the first or the second too. It would double the B/B probability too, but that's not taken in account as we said that one of them is a girl. So: 1. (B/G) 2. (G/B) 3. (G1/G2) 4. (G2/G1) 100/4 = 25 \\ 25*2 = 50%
So I just got halfway through and realised my head was hurting, but thought, “Hey, it’s okay, I’m halfway through - he’s still got half the video to make my head feel okay again”. Then he says “Okay, for anyone who’s still confused, it’s just gonna get worse from here”... Oh boy. 🙄🤔🤯
I know this removes a lot of the subtleties that make this video interesting, but I've finally found a way to understand it intuitively (I was borderline driven to insanity by this video when I found it about 6 months ago, and recently returned to it to try and understand it again!) Just use coin flips: "I flipped 2 coins, at least one of which was heads"- 2 heads would be a 1 in 3 chance, as you could have head tails, tails heads or heads heads. There's a 1/4 chance of getting heads twice, but we're removing 1 of the 4 possibilities by excluding the tails tails result. "I flipped 2 coins, at least one of which was heads, and that one was the bigger one/rustier one/fell off the table", now it's 50/50, because you only need to work out the probability of the other coin being heads as well. Idk why that is so clear to me and the son/daughter situation nearly broke me as a man, but at least now I get it 🤣
Please make a video experimentally testing this! Somehow arrange enough volunteers to fill an adequate sample size of parents who have two kids, and create scenarios with the very particular wording you've described.
This is really, really dependent on how the information is generated. If you ask a couple, "Do you by any chance have a daughter named Julie?" and they say yes, you get a very different distribution than if you first ascertain that they have at least one daughter, then ask the name of one and find out it's Julie. Even though you possess the same facts about the couple and their daughters in both examples, the implied distribution is different.
Correct. In a world where all girls are named Julie, nothing changes. By considering only girls named Julie the size of the sample set (Families with a daughter named Julie) is greatly reduced by the more limiting condition. You are being asked to calculate a DIFFERENT probability. Adding additional information only changes the problem if you are asked to calculate a DIFFERENT probability. Going back to simplest most basic definition of probablility (P=positive examples/all examples), either the numerator or the denominator (or both) must be changed by the additional information to yield a different result. In any problem there are several probabilities that can be considered or requested and it is important to be be very precise about what is being asked.
the apparent paradox has nothing to do with switching what probability is being asked for. the apparent paradox comes from splitting the cases where the sibling is a boy into 2 groups depending on whether the boy was born first or second. it doesn't matter which child is oldest, there are only 2 options; the sibling is either male or female which is a 50% probability.
If I met a guy in a bar and he told me that he had 2 kids and one was a girl the real probability that the other was a girl is 0%. Why? Because nobody would say I have 2 kids and one of them is a girl, the other one is a mystery. If they were both girls he wouldn't say one is a girl.. Oh and hey, so is the other one.. 😂😂 0% is the correct answer in the given scenario. 😜
It's 2019... I think there is a greater than 0% chance that someone somewhere would treat their child's gender as a mystery, because they haven't decided what they identify as yet. LOL!
@@NinjarioPicmin but if the person said something like "my daughter, Julie" then that leaves it open to having another daughter with another name or a son with another name. The wording of the puzzle is for clarification
@@jebadia4518 finds it important to conduct life without regard to irony or humor. Statistically there is a one in thirty four chance that he is a three toed sloth.
I don't understand how seeing the daughter increases the probability to 50%, because, let's assume the daughter isn't like a infant (which would signify that that her sibling is automatically older) but she looks about 10, this means her sibling could be older or younger than her. So the probability is now boy born first and girl born second, girl born first and boy born second, or girl and girl.... this would keep the probability at 1/3...
It's the same situation as the Julie example. If a person has two daughters, then it's twice as likely that you'll see one of their daughters vs if they only have one daughter. Thus, it increases the probability of having two daughters from 1/3 to 1/2
If you flipped two coins, but you dropped one and couldn't read it-- and you looked at the coin you still had and it was tails-- would you be able to then say that there is a 67% chance that the other coin is therefore heads? Because that is what you are suggesting.
@@TheHobgoblyn No, because there you only know that the first coin is tails. That's different from knowing if at least one coin is tails. Knowing that the first coin is tails eliminates 2 of the 4 possibilities, but knowing that at least one coin is tails eliminates only 1 of the 4 possibilities.
I don't really know if I actually understand exactly how this works, but I will try to answer your question anyways: We do not care about their age. Let's say that we call the first child A and the second B. There are four equally likely possibilities: 1: A and B are both boys. 2: A is girl and B is boy 3: A is boy and B is girl 4: A and B are both girls If you observe a child, you know the gender of one of the childs, let's say A. Therefore, option 3 can not be true (as we know A isn't boy). No matter whether we observe the child or not, one of them are always called A and the other is always called B. We can not say that option 3 can also be true, as we might had actually saw child B. They have one name only and always. To understand this, imagine that they have a sign on them reading their name. You observe on of them and you see that it is a girl. You can also read her name, and thus you know what the girl is called. She can't "actually" be called something else, as you can easily read her name on the sign.
If we have two dice, black and white, and have someone roll them and say “at least one gave six” you have 6x6 grid of possibilities with right-down sides of it as suitable ones, only one of them has other also as 6, so probability of ✨other✨ being six is 1/11. When you hear “black rolled six” /“white rolled six”, you have only right side or down side of suitable possibilities, so 6 elements, and probability of ✨other✨ being six is 1/6. The paradox is in word ✨other✨. In first sentence this word means any of two cubes, while in second it mean one particular cube. That’s where the gap is hidden, as I think - more of a linguistically paradox, like “father punched son because he was drunk”
To an advanced alien race millions of years ahead of us, where relativity and quantum mechanics are taught in kindergarten... This problem *might* make intuitive sense 😂🤣
I think I see the problems here... First, if you flipped 2 coins at the same time, and someone hid one of the two coins from you and the coin you could still see was heads, you wouldn't be able to say that there is a 67% chance that the hidden coin was tails. The hidden coin still has a 50/50 chance regardless of the result of the coin you see. Second, your example of people in a conversation-- if a person has 2 children and 1 is a girl AND they mention one of their children at random and the child they mention is the girl, then there is a 50% chance that the other is a girl. Because although there might be twice as many families with 1 boy and 1 girl than there are families that have 2 girls, there is double the chance that if a random child is mentioned in the family with 2 girls that the child mentioned will be a girl. Therefore, in your example of someone saying "I have 2 children, and 1 is a girl"-- the chance of the other being a girl already becomes 50%. Also, if you have a random girl with 1 sibling, then the chances that she has an older brother or older sister or a younger brother or younger sister are all equal. The probability chart does suggest that if you went up to a random person and asked "Do you have two children?" and they said "yes" and then you asked "Is at least one of them a daughter?" and they said "yes", then the chances that they would have 1 boy too would be double the chances they had 2 girls. But at the same time if one were to poll the girls in a class of children who have 1 sibling whether their sibling is a boy or a girl, the numbers would be equal because there is double the chance that the older sister or younger sister is in the class.
After flipping the two coins, you fixed one to be revealed. This is the same as naming one of the daughters, or naming a coin (left or right) to be revealed. If you flipped two coins behind my back and told me at least one was heads, it could be the left, or the right, or both. There are 3 equally likely cases, 1 of which includes two heads.
Almost but there's a total 4 possibillities. We can call the coin you Are talking about coin x om this example. 1 Coin x is heads and coin B is tails. 2 Coin B is heads and coin x is tails. 3 Coin x is heads and coin B is heads or 4 Coin B is heads and coin x is heads. Therefore the the probability is 50%. I understabd what they Are trying to. But not halling the one Coin ore om the video the girl anything, doesnt mean that the girl cant be either the First or second girl/Coin. Thats just nonsensical.
The 33.3% is clearly wrong. The original question in no way requires the ordering of the pairs (in terms of who was born first). That was erroneously added to the conclusion. Even if you include it, there are 4 ordered pairs - (girl first, boy second), (boy first, girl second), (girl A first, girl B second), (girl B first, girl A second). The percentage is always 50%.
yes and if i may be so bold... your 1st and last sentence are all you really need cuz that is the purest truth... "The 33.3% is clearly wrong. The percentage is always 50%."
I believe you are mistaken since you effectively double the probability of 'girl A' or 'girl B' being born first. The first child born only ever has a 50% chance of being a girl, and so if you split that chance between 'girl A' and 'girl B' you would have to attribute 25% to each of them, not 50%. Once you do this you arrive at a probability of 33%. This is similar to rolling double sixes with a pair of die where obviously there is only 1/36 chance, not 2/36.
@Josh Reif Yes the ordering doesn't matter before we have the name (or some other specific identifier, like seeing her in person as was also talked about in the video). And therefore it is -a 50/50- ~33.3%. But as soon as we do get the name, the ordering will matter for the double girl side, but not for the case of the boy being her sibling. This is why it changes to -a ~33.3%- 50% EDIT: Got my numbers mixed around, in the hurry, reasoning is still correct though
@@GummieI Why does the name matter who is born first? It never matters. And the video still says the opposite of what you're saying. From start to finish, the percentage is always 50%
I think the most intuitive way to understand this is the following: It doesn't make a difference whether Julie is the older child or the younger child. Thus let's assume that Julie is the older child (without loss of generality). Now the question is given that the older one is a daughter named Julie, what's the probability that the younger one is a daughter? Now it's clear that the older child doesn't affect the younger child in any way thus the probability of the younger being a daughter is 50%.
the question states "at least one of which is a girl". GB and BG can be grouped together as its own option, since in both scenarions one of the children is a girl. there are 2 options and its 50/50.
I think I get it it. It's about how u word it. For the first one, what it is the chance that the other sibling is a girl given that one is a girl. The equally likely options are: girl that is being talked about, boy. boy, girl being talked about. girl being talked about, another girl. and another girl, girl being talked about. so it's 50 50
This is the correct answer. Another way to think about it is that if someone has a son and a daughter, they have a 50-50 chance of saying either "I have at least one son" or "I have at least one daughter", so this increases the probability that the other child is a daughter back to 50%. The paradox is that the probability of a person saying a statement is not the probability that the statement is true.
Actually, saying I have atleast one daughter consideres and gives information about multiple daughters and I have a daughter named Julie gives no info at all about the other daughter. Similarly, the actual is the same but saying one of which was born on a tuesday gives information combined of one or two daughters and not just a single one. It is when the info given can be attributed to more than one person in calculation is when we get different values.
Them: "I have two children, at least one of whom is a girl" *who says that, by the way?* Me: "What's her name?" Them: "Julie" Me: "Congratulations, 1/6th of your sons just turned into girls."
Something wrong with that paradox. Any random information cannot change the probability. When you know the name the only thihg that has been changed that you know it couldn't be the second one with that name. I am not convinced
@@harshalranjane7669 that's not what that scene about. If you chose that i have pr. 1/3 that i have two daugherts, and after your decision i say "The name of the second child starts with the letter B" you'd better change your decision, because we have new information
K, cool Edit: Actually hol' up , when did this question about sex of someone's child get related to age? Wouldn't (B,G) and (G,B) set be considered same if age wasn't a variable considered? Edit 2: nvm he stated the question wrong
I don't know if that will help you but see things that way : If I tell you I have a two children and at least a daughter and then you ask me if I have a daughter born a monday If I have two daughter the probabiliti that I answer yes is two time bigger than if I had only one girl The information is random but what is interesting is that it exists ( if I have only one daughter it only exist one day where one of my daughter was born whereas if I have two daughter,there are two). sorry for my english :)
@@matteo7123 everithing you said is right. Except the fact it make nothihg to do with the video :D Actually, I found what he did. He mixed up families and girls. When the guy says he has a girl, we decide in wich family he is, with two girls or a girl and a boy. But in this video he transforms it into the situation, when we picked a random girl and trying to find out has she a sister or a brother. And of course it will be 50% chance she has a sister
The problem with your first scenario answer is that nowhere did the question ask anything about birth order. Therefore, the answer is 50/50. You are reading into the question.
There is a subtle error in the video. If you know the other guy has 2 children, and you ask him "Do you have a daughter named Julie?" Then indeed, 50% of the people answering "yes" will have two daughters. However, if every family with at least one daughter makes exactly one statement "I have at least one daughter named X" and families with two daughters randomly select one of their daughter's names for X, then the chance for two daughters is only 33%. The case in the video is closer to the second scenario.
W R O N G "I have two children, at least one of which is a girl" Order 1) Girl + Unknown Order 2) Unknown + Girl The unknown is either a boy or a girl. So... Order 1.a) Girl + Girl Order 1.b) Girl + Boy Order 2.a) Girl + Girl Order 2.b) Boy + Girl Both 1.a and 2.b have the same outcome: Girl + Girl. *>>>>>>>>>>> HOWEVER, THEY DO NOT CANCEL EACH OTHER OUT.
Only if you account for the other pairings now possible with this second female gender you've now created to "fix" the problem... that's gunna get messy
I hope this explanation helps simplify things for anyone confused here... When you say, "Out of two children I have, at least one is a girl, and she has (insert any trait here, we'll call it "X")." , you're not giving two statements but rather three, that being: Statement 1: At least one of your children is a girl. Statement 2: One of your children has trait "X" Statement 3: (Most importantly) Child with trait "X" is a girl. If you have said, "At least one of my two children is a girl. One of my children has trait "X"." It would be like the first sentence, only difference is that Statement 3 isn't included here. And this what most people think when they say, "Why would a random trait affect the probability regarding their genders, they're unrelated!" However, with the sentence in question here, because Statement 3 is implied with the words, " and she has trait "X"...", a direct association between the child's gender and trait "X" has been made. This then allows trait "X" to be a relevant factor even if the question was about gender, because Statement 3 links the two together. Had Statement 3 not been made, trait "X" would be irrelevant.
Absolutely true. The real key to the "trick" is the phrase stating that "at least one is a girl", which never identifies which child is associated with that trait (gender) and thus there are still 3 possibilities. The moment they link that trait (e.g. "my oldest child is a girl", or "the girl is named Julie", or any other possible linkage) then the possibilities drop to only 2.
It's only counterintuitive because the question is based on a false assumption. I've seen this done many times - the question is framed wrongly. You ask "What is the probability that the other child is a girl?" This question implicitly is based on the assumption that beforehand, we were talking about one specific child out of the two, or else "the other" wouldn't make sense if we weren't talking about "one of them" before - which we weren't! So using that phrase means the question is based on a false assumption. This is exactly where the counterintuitivity arises. Correctly, the question should be "What is the probability that both of them are girls?", which is less counterintuitive.
If someone says "I have 2 children, at least one of which is a girl" to you, just smile and walk away slowly without turning your back, because who actually talks like that outside of math and logic problems.
The given method seems to base its numbers off looking for the number of Julies in each group and finding 250 in the boy&girl group and 250 in the 2 girl group. This doesn't make sense because if the parent has two girls and gives one name, they would have to choose one or the other and can be assumed to choose at random. Of all the two girl groups with name Julie, the parents would only be expected to choose Julie's name to give 50% of the time and thus only 250/500 2 girl groups with a Julie would say Julie, compared to the 500 Julies in groups with one girl whose name would be stated every time. The 50/50 probability is incorrectly double counting the number of Julies that would be mentioned in the 2 girl groups, because one of the two is randomly selected. Therefore I believe the probablity in fact never changed, remaining 33.3%.
That's not how children's names are chosen. Your model isn't correct because nobody starts off with two children and decide which one to name Julie. What actually happens is, they have a first daughter, where 25 people will decide to name her Julie, just like those who have 1 girl followed by 1 boy. Then they have a second daughter, where 25 additional people will decide to name her Julie, just like those who had a boy first then a girl. That makes a total of 50 families who would name one of their daughters Julie.
@@letao12 I believe that Trey B is referring to "giving a name" as the guy at the bar telling you the name of one of his daughters, not how the names of daughters are actually decided at birth.
Ah I see, sorry I misunderstood. In that case the other 50% where the guy doesn't name Julie is irrelevant to the problem. Basically we want the conditional probability of 2 girls given that the guy has already named Julie. Naming Julie is a prior condition. The chance that they don't name Julie is excluded by the prior.
Okay I like the analysis but have a follow up. Let' assume half of the girls out there are named Julie. Now given 2 families, each with 2 girls, wouldn't we expect both of them to have a daughter named Julie (since you'd take half of 4 to get 2 girls, then assuming no overlap that means 2 families)? But your analysis would assume only half those FAMILIES would have a daughter named Julie, which means there'd be 1 Julie out of 4 girls, which goes against our initial probabilities.
I went to an abstract bar and tested it (try running it yourself, it's javascript): // boy and girl tally var bNg = 0; // 2 girls tally var gNg = 0; // sample size var sample = 1000; // loops through sample for(let i=0; i
As I see it, there are two distinct situations. first which he says: 'I have a girl named Julie' two which he says: 'I have a girl, her name is Julie' (in both of them he says: 'I have two children') In the first one: the logic of the 50% works, because you learn of a girl named Julie. In the secon: the 'name information' is pointless, as it is given as information about the daughter. Information which she obviously has.
4:04 actually you assumed families can name both their daughters Julie when you made it 5000 girls in total, if 50 of them are named Julie there are 50 other girls that cannot be named Julie (their sisters) which you didn't take into account at all. If you make an assumption it should be made before the calculation, not somewhere in the middle
This is the Monty Hall Problem repackaged. The "paradox" is that you're shifting from an unconditional to a conditional probability without stating it outright.
"I have a daughter named Julie." Only restores the parity if there was something special about the name Julie which prompts the respondent to consider the names of both his/her daughters. If he was asked to randomly select one of his daughters and then confirm if that selected daughter's name is Julie he might answer "no" if he has two daughters, one of whom is named Julie, but it isn't the one he selected.
I'm throwing the 'shanagans' flag on this play. The names and birth order are irrelevant to the core question, "what is the probability of my other child being female?" All the extra information in the world does nothing to change an isolated variable. It doesn't matter that given girl likes liver flavored ice cream and has a crush on Chris-Chan. The reason everyone fights over this is because the question is worded such that it is deliberately vague and without absolute reference frames. TL:DR - doesn't matter how she's a special snowflake, it's still 50/50 (Or 52/48 if you want to be technical about it).
The probability is 50% no matter once. Naming the daughter only dignifies her as a separate person in our brain. When we are told that he has one daughter, even thought a name is not given, we can label this daughter daughter 1. There fore there are these possible cases: daughter 1 + son/ son +daughter 1/ daughter 1 +daughter 2/ daughter 2 +daughter 1. This makes a 50% chance. The paradox only roots from a cognitive bias of labels in our brain. Though we do not naturally label someone if we are not given their name, they should still be dignified. If we simply label them both girl there is nothing showing the difference, therefor we ignore an entire possibility.
(Sorry for my bad Englisch) What you do is: You change the perspective of probability. I give You an example. When You give the girl a Name, You calculate the probability if a that Girl have a sibling wich is a girl or an boy. The same ist with a weekday, or day in moth, You always change the perspective, and that matters for the calculation. You know that, I guess. Really nice video.
I believe there is a slight mistake in the video. Zach Star, please correct me if I am wrong but it would be helpful as I'm doing Further Maths this year! Basically, I think the mistake is in the question. If you say you have a daughter and she is, in scenario 1, the younger of the 2 siblings, then the other child can only be a boy or a girl, meaning the probability of the other child being a girl is 50%. In scenario 2, if the girl is the older sibling, the younger sibling can STILL only be a boy or a girl. Sometimes, if you have the pair A and B, that is considered to be the same pair as B and A. So why does it not apply to the concept whether a boy is born before a girl? What I mean is, if we label the pair of children/siblings B (boy) and G (girl), then wouldn't the pair B&G be the same as G&B, leading the 2 out of 3 options to cancel out to one out of 2?
This is probably really late, but essentially what we don't know is influencing the results. Say we flip 2 coins. there is a 50% chance coin 1 lands on heads, and a 50% chance coin 2 lands on heads. The probability that both coins land on heads is 25% (50%*50%). Easy so far. The options for what we can get are currently: a. Coin 1: heads, Coin: 2: heads b. Coin 1: heads, Coin 2: tails c. Coin 1: tails, Coin 2: heads d. Coin 1: tail, Coin 2: tails In the example in the video, we can substitute heads for boys and tails for girls, firstborn for coin 1 and second child for coin two. It's now: a. firstborn: boy, secondborn: boy b. firstborn: boy, secondborn: girl c. firstborn: girl, secondborn: boy d. firstborn: girl, secondborn: girl We can now cross off the option of both boys, as we know at least 1 is a girl. -a. firstborn: boy, secondborn: boy- b. firstborn: boy, secondborn: girl c. firstborn: girl, secondborn: boy d. firstborn: girl, secondborn: girl alas, we can see that exactly 1 option is both girls. Essentially what is happening, is that x, y and y, x are different things, because they each have their own probability of happening. (25% for both boys included, 33% if not.) I hope this helps.
@@SnowRose-wn6gj This whole video is utter nonsense. It's like the wrong solution to the monty hall paradox. The first child has already been revealed. The original set of outcomes and combinations no longer matter, only the new set of possible outcomes with the information revealed. Which means it's 50/50 always in every example.
Not only this is counter intuitive, it's wrong. The order of birth, doesn't influence the result of your initial question. This is just gimnastic to get views on youtube. SAD.
I'm reminded of the 10,000 people, including nearly 1,000 with PHds, who wrote letters to tell Maryland vos Savant that her solution to the Monty Hall problem was incorrect despite her being demonstrably correct. SAD.
The real answer relies in WHO asked you the question. In 100 families, all with 2 kids, at least 1 of which is female, 33 families will have a second female. If a parent asked you, assuming there are the same number of parents in each family, the answer is 33%. You have run into a parent of one of these families that have 2 kids and at least one daughter and 33/100 of them have a second daughter. The odds the parent you ran into is a parent of a second daughter is 33%. However if one of the children tell you the riddle, it is either a 50% or 0% chance. If a girl in the family tells you the riddle, it is 50%. There are 150 girls in this scenario and 75 of them have sisters. So there's a 50% chance you ran into a girl with a sister. Obviously if you run into a son of the group, your chance is 0%, because he isn't a girl. Now if you ran into BOTH the parent and daughter of the same family, you can fall back to the "family" stat of 33% because although for any given girl the number is 50%, you ran into a parent. And for any parent, the 1st girl was already a given. It's not really different probabilities of a second girl existing. The same number of girls exist the whole time. The probability is that of who did you run into? In other words, in a family of 1b,1g, there are 2 parents to 1 girl. In a family of 2g, there are 2 parents to 2 girls. The 2nd girl exists half the time, but the existence of the girl does not magically add more parents for you to run into to ask you the question.
I came up with exactly this seemingly paradox myself and I felt really proud when I did. It really comes naturally when you do the maths, because the only reason that the probability is 1/3 is because there is nothing that allow you to tell one child apart from the other. It’s basically 2 random variables X and Y but no idea who’s X and who’s Y. So I thought, if the father add « Her name is Name » then you can have 2 random variables : X and Name, and you can tell them apart and the probability changes to 1/2. In some kind of way, I feel like it ressemble quantum intrication : in the first situation, the information you have on the system is greater as a whole than within its parts.
The second problem is faulty, ‘Julie’ is a random value and could as well have been any other girls name. This means the answer is still 1/3. Perhaps if the other 9900/10000 girls were all nameless this would work.
Even in the case where you ask if one of them is named Juliet, it still isn’t 1/2 if 1/100 of girls have that name. The second child would have a 99/199 of being a girl as you remove the Juliet’s from the selection pool.
“I have two children, at least one of which is a girl.” What is the probability that the other child is a girl? The birth order of the two children isn’t relevant information in that statement or the question, so the answer is 50%. It’s either a girl and a boy, or two girls. It all depends on how the question is asked. If it instead it was: "You will have two children later in life, one of which will be a girl. What is the probability that the other child will be a girl?" Then yes, the answer is 33%, because there's four outcomes of Bb, Bg, Gg, Gb, and like you said, Bb can't be an answer. But by stating one child is a girl before the question is asked, the probability becomes a simple coin toss to determine whether the other child is a girl. In other words, the two outcomes of Bg and Gb are the same thing if birth order is irrelevant.
You are right because the I in "I have two children" also give information. Making the order of birth on the two children not relevant. Shifting the analysis from global population statistics to "biological/binary permutation" (Probability of said person to have)
Yes you are right. As a multilingual person I can easily understand this while I see so many people in this comment section struggle. Edit: I also want to say your example is brilliant.
no this is all wrong. imagine 4 couples with two children each Bb, Bg, Gg, Gb. 3 of these couples can correctly state “I have two children, at least one of which is a girl.” but only 1 out of those 3 have two girls. the probability works the same way given just that information for a random couple.
@@shiinondogewalker2809 But why imagine 4 couples when the first part says "I have two children" lol Predicting the future birth order of two children (Bb, Bg, Gg, Gb) doesn't apply here because the question is in the present tense: "I have two children" rather than "I will have two children." Basically, the difference between the present and future tense of this question is why the paradox exists.
This probability paradox is actually a way to understand quantum mechanics. Whether there is one girl or two girls represents the state of a particle, while giving the name of a girl represents observing a particle. Observation really does change probabilities.
With the first statement as you rightly said there are 3 possible options: GB BG GG => P(G,G) = 1/3 However with the additional information => ".. whose name is 'X'", what is happening is identifying a specific individual in the "GG" possibility. This identification implicitly splits that as two possibilities => G'G and GG' : where G' is the girl with name 'X' This will make the possibilities: G'B BG' G'G GG' => P(G'G | GG') = 2/4 = 50% In a sense this identification is similar to saying "boy or girl" instead of saying "child". Specifying an identifiable attribute splits up the probability space.
The error is right in the beginning, when the question is, "I have 2 children, at least one of which is a girl. What is the probability that the other is a girl?", we have 2 cases: _Case 1_:- They are talking about the *child other than the girl*. In this case, since it has *ALREADY BEEN ESTABLISHED THEY ARE TALKING ABOUT THE GIRL*, the only possibilities of the combination is GG/GB, since there is *ONLY 1 SPOT TO FILL*, so the the probability is 50-50. _Case 2_:- They are asking the probability of the second child being a girl, when *the first child is randomly picked*. In this case, we either choose a boy or a girl for the first outcome, but only a girl for the second one. So, the total outcomes are GG/GB/BG/BB, and we choose GG/BG, for a probability of 50% again. TL;DR- The error arises in him considering only GG combination and not considering all of the outcomes, probability is 50% either way.
I bet if I flip a coin 9 times and get tails all 9 times you'll still tell me the probability of the next flip is 50%. But what if i told you that the first coin had lincoln on it, does that change the probability?
I clicked on the video thinking "If it's Monty hall problem I'll probably click off..." Then I thought "Yup, Monty hall problem, but apparently there's more..." Then I stay until the end and there was way more than the original Monty hall problem. Thanks for sharing this with us!
The answer is simple: It's not 33% , the probabilty is 50% because: There is 1 out of just 2 posibilities 1. gril and girl 2. boy and girl ( boy and girl or girl and boy is the same thing. it doesen't matter in this is case wich was born first, because that's another condition wich is not stated in the question ) 3. boy and boy is not valid I give you a simpler example with the same question •From a store with only red and black cars I bought two cars, at least one of wich is red • What is the probability that the other car is also red?
There is no paradox whatsoever. Its 1/2 no matter what. There is no "boy, girl; girl, boy; girl, girl". Its: boy, girl; girl, boy; girl, girl; girl, girl; because the two girls arent the same girl. And you dont have to know anything about the girls to know that. Its clear from the beginning and thats why intuitively people will say the probability is 1/2, which is correct. Not 1/3.
@@zachstar So your odds of having a boy or a girl at any given time are 50/50 but having two girls in a row is only 33%? I don't understand how naming or pointing at the girl changes that.
@Bo Dodge, no I'm saying if I ask you if you have at least one daughter and you say yes then I have a 33.3% you have 2 daughters (this wasn't what I said in the video but I've corrected it in the pinned comment and the follow up video).
The fault arises when you assume that a family cannot have two daughters named Julie and that a boy cannot have the name Julie. This changes the data provided and makes a seemingly unrelated piece of information (name) vital to the problem. You cannot change between working with purely theoretical numbers based on a perfect world (where both daughters and sons can be named Julie) and working with numbers that are based upon the norm of parental naming choices. If boys can be named Julia and a family can have two daughters named Julie, there would be no paradox.
Not really. These data and their inferences actually DO matter. However, when stats are presented to the general public, the journalist should present the forest and not the trees. Going a little off topic here: Instead of mentioning homicides have increased since the 1900s, they should take into consideration the fact that the population has increased and that reportings have increased which might even explain away and real difference in homicides. Journalists love to hype/exaggerate scientific findings. Coffee is good/coffee is bad. Wine is good/wine is bad. Wine is terrible for your health and coffee is good but I digress. The nuances do change everything and (correct) math is the truth.
@@itsover9008 Yes really. The odds of a fair coin having landed on heads is 50/50 every time. Learning other information doesn't change physics, or genetics, or anything else. The likelyhood of an event doesn't change by learning information, ever. The likelyhood of having two girls is set by genetics. Hearing about the name or hair color or age doesn't change that. Genetics doesn't change because you learned something that you didn't know before. Statistics tries to change genetics by learning what the girl's name is. Something you learn early in your scholastic career is to weed out information that doesn't impact what you're looking for. Statistics tries to turn that around and make use of useless information.
@@theofanislantzakis9869 You're right. Statistics isn't the problem. People not understanding what information is useful and what isn't is the problem. The name doesn't matter at all.
@@atheistontheroad4545 thats not 100% accurate either.. the name or not name could be important or not.. the problem is in the fact that the probability has no real bearing on the outcome. weather its 33% or 50% doesnt mater since the only outcome that matters is the one that is true. Changing and adding information that changes the percentage is irrelevant to the end result.. you could add information until its 99% that is 2 girls or 1% that its 1 girl but either way either outcome is possible. in reality everything has a 50% possibility.. 1 it is or 2 it is not. but numbers and information can be moved around to determine a likely likelihood.
Actually thought of a great analogy to explain this: Imagine you're on a beach, searching for yor daughter. You see two people in the distance, and although you can't make out the details, and you're not sure who's closest, you're sure at least one of them is a girl. We then have 3 possibilities, (G,B), (B,G), (G,G), the one on the left being the one closer to you. You get a bit closer, and although you still can't determine who's closest, or the gender of the other person, you're difinitely sure that the other one is your daughter. Now, again with the closest one on the left, we get this distribution: (D,B), (B,D), (D,G) and (G,D). In the first case, only one outcome of the three gave us two girls, but in the second one, it's two out of four. Not sure how helpful this is a year later but i had to share. (B stands for Boy, D for daughter and G for girl)
I think you explained some things a bit wrong. Anyway here's how this intuitively makes sense: a parent in a family with 2 children casually mentioning the name of their daughter is is bigger if they have 2 daughters, if they have one of each they could have mentioned the name of their son first in which case you know its not a family with 2 daughters. Even by saying "my daughter's name is..." they have already revealed that they have a daughter before revealing they have a son. Any mention of a daughter increases the chance of having 2 simply bause families with one of each have a 50/50 chance of mentioning their son first.
@Peter Rabitt the order definitely does matter for this. A family of 2 kids can have either BB, BG, GB, or GG. That isn't an arguing point that's just how this question is set up. So when you know that at least ONE is a girl, you're narrowed down to BG, GB, and GG. Of which, only 1 of the 3 has a girl as the other sibling
@Peter Rabitt if a flip 2 coins and tell you ONE is heads, what is the probability the other is also heads? By your logic it's 50%, which is clearly not right
@Peter Rabitt let's think about real life real families with 2 kids. A family can either have a boy as their first and a boy as their second, a boy as first girl as second, girl as first boy as second, or girl as first girl as second. There is no other way to have girls and boys, that's it. Now since they all have equal probability, the BG and GB as a whole group will be twice as much as just the GG group.
It is not surprising to me. There is extra information in the 'her name is Julie'. The extra information allows us to reasonably assume the other person is not named Julie, and this assumption changes the context thereby changing the calculation
There is a layperson's language problem here. We often talk about "The Probability" as if that is a single concept. But the discussion is about "The Probability of x, *CONDITIONED ON* the following information". This is comparing Red Apples to Green Apples (not quite Apples to Oranges). They are different situations, and of course can measure differently.
I guess we shouldve assumed the probability of both born on Tuesday is greater than 1/49, but we'd have to know the probability of twins to get the exact number
I'm going out on a limb to disagree about this video. In my eyes, the dice were rolled WHEN the children were born. Thus, those odds are the ONLY thing that matter to their gender. Not name, date of birth, or anything. As none of those varibles affect the original dice roll (odds) of it being GG, GB, or BB. I feel like our brains are logically wired to disagree with this line of thinking, but... The more I think of it this way, the less I agree with the video's math and the commenters' logic.
This reminds me a lot of the Monte Hall Problem. For those of you who don't know, there are 3 doors, let's say A, B, and C. You pick a door, then the host then shows an incorrect door, the asks if you should stay, or switch. Most people think that you then have a 50/50 chance of winning (most people choose to stay partly because of this), but they are wrong. By switching, you have a 66.7% chance of winning, with a 33.3% chance if you stay. This is because in the beginning, you only have a 33.3% chance of getting it right, and because the host will always pick an incorrect door to reveal. The fact that the host always picks an incorrect door, you still only have a 33.3% chance you chose right. If you still don't get it, I'll lay out all the options. Let's say Door C is the winner in this case. Pick A -> B is revealed to be incorrect -> Stay -> Lose Pick B -> A is revealed to be incorrect -> Stay -> Lose Pick C -> A/B is revealed to be incorrect -> Stay -> Win Pick A -> B is revealed to be incorrect -> Swap -> Win Pick B -> A is revealed to be incorrect -> Swap -> Win Pick C -> A/B is revealed to be incorrect -> Swap -> Lose As you see, if you stay, there is only 1 out of 3 possibilities you will win, while if you swap, there are 2 out of 3 possibilities you win. I don't know why, but I like explaining the Monte Hall Problem.
At 10:41, the correct phrase would be "15 percent points", not "15 percent" as you said. Nice topic though! It is counter-intuitive on a superficial level only. Because, the whole idea of probability theory pivots on the idea that the more information you have the more accurately you can calculate the probability. Hence the change of figure. To anyone familiar with Bayesian way of reasoning, this phenomenon would not appear weird at all.
Information not in evidence was assumed, however. Firstly, that all of the pool of b/g//g/b families would indeed refer to their daughter rather than their son. Given no data to support that, the appropriate hypothesis is that half of those families would refer to their son instead of their daughter, and since the man in question referred to his daughter, his family is not one from that pool. Accounting for what information would be shared by de-biasing where information was not given to support the bias gives us 50%s across the board.
I think you didnt understand it right so you are confusing us. Your calculations were right, no complaining on this. We have two numbers: 50% and 33%, which you can say both are correct answers, but for different questions. The probability that you have two daughters is 33% but the probability that julies sibling is a girl is 50%. So you asking where does the probability rise. Its not like you presented it. When he says I have a daughter named Julie, the probability that he has two girls is still at 33%. Lets assume you meet one daughter, then there still could be the possibility that this isnt Julie, but when you get the information, that this is Julie, then the probability rises to 50%.
Let me make this very simple to understand. In the first explaination is the error. You need to count the number of 'girls-with-a-sister' in GG column as *500 instead of 250* because both girls in each element of GG have a SIBLING WHO IS A GIRL.. you can't just count one set of girls to have a girl sister, the other set of girls *also has a sister* by definition. (Reversible relation) (the same way you did in the 'Julie' example.) Which makes all 500 of the elements in GG each have a sister-sibling (as opposed to only 250 girls having a sister-sibling). So there are 500 'girls-with-a-sister' in 250 families of GG. And 500 'girls-with-a-sister' in 500 families of BG. Now's the easy part! We have Event (E) = One of the children is a girl. P(G/E in BG) = 500/1000 = 50% P(G/E in GG) = 500/1000 = 50% Hence a 50% chance of having a girl sibling in GG family as well. Or easier way to say it is, there's a 50% chance of having a girl child *if one of the two is already given to be a girl* There! Now there's no paradox :)
"I have 2 children, one of which is a girl"
"So is the other one a boy?"
"No, the other one's a girl too."
"Then why didn't you just say that?"
"Alright, I have 2 girls, one of which is a girl."
This comment actually made me laugh out loud. Thanks for that!
the other is what anitubers like to refer to as a "futa"
When statisticians and sociologists make small talk? ;)
2 kids with whom your wife or girlfriend?
You need to specify these days. lol
@@DSiren A man of culture I see
The change of probability from 1/3 to 50% is, in fact, based off the fact that the focus of the analysis has moved, with the introduction of new information (the name) which pertains to a population (daughters) which differs from the starting one (families).
To exemplify this, I'd draw your attention to 2:15. This question can be easily rephrased to give 50% as a correct answer. Let's look at the information you provide in terms of children, rather than families. With 1,000 families with 2 children each, we have a total of 2,000 children.
These can be represented as follows:
[notation: (X|Y) means persons of gender X given their sibling is of gender Y]
500(B|B) [or 250(B,B) pairs];
500(B|G); 500(G|B) [or 500(B/G,G/B) pairs];
500(G|G) [or 250(G,G) pairs].
If I now asked "what is the probability of this girl's sibling being a sister?" the answer would be 50%. In actual fact, we'd have 500 girls with sisters, over a population of 500+500 = 1,000 girls. Both answers are correct: 1/3 of families with a daughter have two, and 50% of girls have a sister.
Looking at the problem at hand, the issue is that the information "1% of people named 'Julie'" (note: the issue is not the name, but its assumed distribution) is disproportionately applied to the girls population - ie, 1% of (B,G/G,B) and 2% of (G,G) are taken. What you are therefore answering is "what is the probability of this girl named 'Julie' having a sister?". The answer remains unsurprisingly 50% as above.
It is therefore incorrect, in my opinion, to disproportionately apply this to the siblings pairs, in that you are moving your focus from the families to the girls. To see this, we can change the problem slightly: if the assumption drawn from the name was that "1% of *all families with a daughter* name their daughter 'Julie'", you'd end up with your probability of 1/3 - as before.
We take our 10,000 families. 5,000 are (B,G/G,B) pairs; 2,500 are (G,G) pairs. 1% of all families name their children 'Julie', so 50(B,G/G,B) pairs would have a person named Julie in them and 25(G,G). 25/75 = 1/3 as before.
Massively underrated comment
This do b the answer thx
Nice explanation.
Stipulating that 1% of all families with a daughter name their daughter Julie does not change the way in which we might expect the names to be distributed. If one family has two girls, and thus two opportunities to name a child Julie, then we would typically expect that two-girl families are twice as likely to have a child named Julie than families with only one girl.
@@James-rq9qb Ah, but you see, with your assumption you're providing additional data on the distribution of the name Julie.
Up to that point I know that the family have a daughter, whose name is X, where X has an unknown distribution.
When I'm told that X = 'Julie', 'Julie' still has an unknown distribution until I observe that this is not the case - and I'm told nothing in this regard - making the information effectively useless. The distribution does not follow from receiving the name. It follows from looking at a population sample and take very meaningful measurements, which do affect your probability space (ie, you're literally counting how many families with a daughter have a 'Julie' in them and how many families with two daughters have a 'Julie' in them).
When you say that families with two daughters are twice as likely to name their daughter 'Julie', you're describing a behaviour that, albeit of common sense, does not mathematically follow from anything you've been told. You're therefore introducing new information in your analysis through a behavioural bias.
Say, for example, that the daughter was named 'Alex'. As this is a gender-neutral name, I could make no educated guesses as to how this would affect my analysis. However, I could go in the population of families with at least a daughter and two daughters, and measure how many had an 'Alex' in them, adjusting my final conclusions.
You are not fully correct. The disproportionate chances of "Julie" appearing in (BG,GB) and (GG) pairs is only part of why this happens. It becomes more clear, what changes if you give a direct mathematical formulation:
Let X1 and X2 be two identically distributed but not independent random variables. Let P1 be a predicate such that P1(X1) is true with chance 1/2 and likewise P1(X2) is true with chance 1/2 (the gender). Also, let P1(X1) and P1(X2) be independent.
The statement that leads to 1/3 chance is: Given that P1(X1) OR P1(X2) ("one of them is a girl") is true, what is the chance that P1(X1) AND P1(X2) ("both are girls") is true.
Now for the "Julie" case: Let P2 be a predicate, such that P2(X1) AND P2(X2) must be false (can be ensured by X1 and X2 not being independent). Also, let there be a non-zero chance that P2(X1) is true and a non-zero chance that P2(X2) is true (those are the 1% of Julies in the population). Given that (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), what is the chance that P1(X1) AND P1(X2) are true? The answer is 1/2 because the chance of P2(X1) AND P2(X2) is zero.
Now the "Tuesday" case: Let P2 be a predicate, such that P2(X1) is true with chance 1/7 and likewise for P2(X2) with P2(X1) and P2(X2) being independent. Given that (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), what is the chance that P1(X1) AND P1(X2) are true? The answer is 13/27 because the chance of P2(X1) AND P2(X2) is 1/49 and therefore larger than zero.
Here one more obviously sees the differences between the Julie case and the other cases. It all depends on the probability of P2(X1) AND P2(X2) being true (zero in the Julie case, non-zero in other cases). In fact, I believe it should be possible to factor out this term somewhere from (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), but I cannot quite get this to work currently.
Also, by setting the probability of P2(X1) AND P2(X2) to arbitrary values, one should be able to get any probability between 1/3 and 1/2 (although I cannot proove this directly). Imagine a scenario "I have a child, one of them is a girl who has this hereditary disease that co-occurs in siblings with a chance of p". Then this would further change the probability of P1(X1) AND P1(X2).
In the case where you get 1/3 chances with the girl naming Julie, you are changing another aspect of the puzzle. Now you are modifying the probability of P2(X1) OR P2(X2) (meaning the total chance that a family names one of their children Julie). Because this term also appears when factoring (P1(X1) AND P2(X1)) OR (P1(X2) AND P2(X2)), it changes the probability back to 1/3, although P2(X1) AND P2(X2) still is zero in this case.
Rando: "I have two kids. One's a girl, born on a..."
Me: "13/27ths!"
Rando: "... boat."
I'm pretty sure this changes everything because you don't let this happen twice. Except you're a Kardashian and need that social media stuff.
The enunciation needs to be a bit clearer, but I see where this could be going.
we'd have to start with the event of both kids being born at the same time.
which is funny... really... because it seems like nobody actually has a damn clue about that... or none that I could find.
that will be the basis of our probability distribution.
we will say we have a probability W1 for not twins and W2 for twins ( and of course, they add up to 100% )
for the W2 case, it's a 25% of having 2 girls, so overall that is W2 / 4 in our situation
for the other one tho... we will suppose that if they are not twins, the other kid was not born in a boat, so it bares a Julia case distribution... therefore W1/2
Case solved (ish )
Ok, ok... the chance of having fraternal twins... is 1/125 ( suggests a source on a math forum, take this with a grain of salt )
in that case, we have a chance of 62/125 + .25 / 125 which adds up to 62.25 / 125
god save us all
0.498
yaay...
And her name is Boaty McBoatface
Wow, that's almost exactly what I said to myself when he paused just after 10:57 ! For some reason I chose "lifeboat" for what I thought he was going to say.
Although, I think this shows why the probability doesn't change until they quantify that new piece of information. Not for watercraft, because apparently that's common enough that we both jumped to it, but if they were to say "leap day" then we really know the probability would be lower.
The very fact that she was born on a boat will also increase the probability to 50%, just like in the case of Julie
If someone tells you they "have two children, one of whom is a girl named Julie", you can't really make the assumption that they're not weird enough to name both their daughters Julie.
True
Haha true
If all girls were called either Julie or Zoe, evenly distributed and with no same names, 100% of the 33% would have a Julie but 50% of the 66% would have a Julie. That's a better explanation I think
But maybe you can assume they're not so weird as to tell you one of them is named Julie if both are.
@@carllorenzandonaque9242 Nitpick #1: It matters how common the name "Julie" is. If we make the same illogical assumption that lead to the 1/3 answer - that you can't know "I have two children, and at least one is a boy" for any family that has a boy and a girl? Then the answer is (2-J)/(4-J), where J is the frequency with which girls are named "Julie."
This is the answer that Leonard Mlodinow gets, but I don't think he put it in "The Drunkard's Walk." He just said "close to 1/2." But he has said it on forums. Note that if J=1, this is 1/3, the answer he got without the name. And as J approaches 0, it approaches 1/2.
Nitpick #2: The assumption that you can't have two Julies in the same family also means that you can't have two Marys, two Anns, two Constances, or two Sunshine Angels. That really throws a wrench in the calculation. And it turns out that if the name is rare - as Mlodinow did, he used "Florida" - the chances of another girl are actually greater than 1/2, not less. This is because the rule affects very few families, so a two-girl family is essentially twice as likely to have two "Floridas" as a one-girl family. But the high chances that a first girl has a common name like Mary reduces that. The answer is close to (1+A-J)/(3+A-J), where A is the frequency of the average name.
here's a way to rephrase the questions that makes intuitive sense:
the first question is "given that I have 2 children, at least one of which is a girl, what is the probability that they are both girls?"
the second question is "I have a daughter. What is the probability that her sibling is a girl?"
the first question is conditional probability
in the second question, despite the fact that you can mince words to make the questions virtually identical, you are only asking about the probability of one specific person's gender
this is a good way to phrase it
no because that changes the focus of the whole question
@@darbyl3872 I flipped two coins, one of them came out Heads. This gives you 4 scenarios (HH, TH, HT, TT) There are 3 scenarios that have one H and of those 3 you have 1 of them being double H. (So you have 1/3 - 33% - The first question)
I flip a coin. It's Heads. I flip a second coin. What is the probability of it being Heads? (Since you don't care about the first coin anymore you just have to guess what the second is - 50% - the second question)
@@TheRandomYoYo that makes a lot of sense. Great way to put it
There is no functional difference in these questions. No mincing of words required.
Professional statistician here: I can explain this. The issue is that the math in this video is subtly wrong. Here is why:
You have to be really careful about probability, and particularly about conditional probability when you suddenly introduce new information: What does this do to your probability distribution and what does it do to your sample space?
There are actually two situations here, and they are actually different.
1) You ask a guy: "Do you have a daughter?" He says "yes". You then ask "What is her name?" and he says "Julie".
2) You ask a guy: "Do you have a daughter?" He says "yes." You then ask "Do you have a daughter named Julie?" And he says "ZOMG you are a wizard! Yes I do!"
In the first case, the probability of him having a second daughter is still 33% as before, and in the second it is 50%. This can be thought of as follows: In the first case, if the guy has one daughter named Julie he will name her, but if he has two daughters he might name Julie, but he might also NOT name Julie and may name the other one instead. This means that if he has a daughter named Julie, he might not always tell you this. In fact, he will only tell you so 50% of the time, which reduces exactly to the case when you don't know her name: Most of the time he will only have one daughter.
In the second case, the probability of him having a second daughter is 50%, and this is also somewhat intuitive. You just did a pretty shocking bit of guesswork with her name, but your guess would have had a better chance of success if he had two daughters than only one, right?
The same thing works for Tuesday, pretty much exactly the same way as in the name situation. For physical presence it is slightly different, but the reason is still somewhat similar. The "there she is", might be enough to get the 50% answer form the video. We have to understand the distribution of people who are there. For instance, imagine you are sitting there and there are two kids, a boy and a girl, and he points to the girl and says "there she is". Do you still think there is a 50% chance the other is a girl? How about if there are two girls there and he points to one of them? How about if there is only one other person in the room and it happens to be his daughter? Note that these situations are all different from each other.
EDIT: OK I just saw that this was addressed in another video by the same guy. I still want to leave the answer up though, just in case someone does not find the other video.
tuerda I’m a graduate student in statistics. Another issue I have was the subtle assertion that if one daughter is named Julie, the chance of the other being named Julie is zero. This reduces the sample space entirely to a conditional sample space on the other daughter. This changes what was previously a combination to a permutation, where only one spot in the permutation is unknown. This is the chance that one kid is a girl, 50%.
@@Creshex8 Yes, there are several odd modeling assumptions, but they are not the cause of the apparent paradox.
tuerda you sir are very intelligent
You don't get the core of the problem which is that probability theory doesn't apply for these examples.
Which is funny given that you claim to have a profession in a related field. Obviously that profession prevents you from seeing clearly.
The question the video asks is not a probability question. You need a repeated experiment to claim any probability. The probability is determined in the construction of the experiment.
None of you (you and the video maker) have described any actual repeated experiment, so there is no answer here.
@@StefanReich The meaning of "probability" is a messy philosophical question. An extremely frequentist stance does require repeated experimentation, but this is not the only interpretation (nor, for that matter, even the most popular one anymore).
The wikipedia article on "probability interpretations" reasonably sums up the complete chaos involved arguing about what probability is. I can elaborate or give you further references if you like, but this rabbit hole is **deep**.
Man: I have two children, at least one of which is a girl.
Me: Yeah, these are confusing times when it comes to gender.
Man: I have two children, at one of which is at least girl. She might also be a boy.
What if I have two kids, one that is a girl named George, was born on a leap day February 29th, does not like ponies and only regularly keeps a diary and rather eats corn flakes than rice crispies? I think we can all agree that chances of my other kid being a boy is infinitesimal at best. Nearly 100% probability the other child is hermaphrodite, lift up the scrotum and there's a big ugly cooch behind.
Rex yes!
@Aditya Panda could be either or until we observe it
Man, that is brilliant. At least one of which is a girl …. Ive calculated how much i spend on clothes.
Coworker: It's my daughter's birthday.
Me: HOLD ON I GOT THIS
Great it's 11pm here and I'm watching this. Not gonna sleep tonight I guess...
2 am😎
4 am😎😎😎, thanks to covid-19
Me too.
you guys sleep ?
Midnight here
I feel this is approached from a strange angle - the idea that the probability is based on if the older sibling is the girl mentioned or not. The question is simply "What is the probability of the other child being a boy or girl?" then it truly is 50/50, since there are only two, equally probably outcomes. The paradox in the video only comes into question because they're assuming that
A) In the pool of numbers the probability stems from that there is an equal number of boy/boy, boy/girl and girl/girl options but that there are also additional options of which one is the older/younger sibling.
B) That the older sibling/younger sibling pairing counts as a separate pool to draw probability numbers from, even though that factor is entirely irrelevant to the initial question.
If the question was "What is the probability of the other child being a girl and the younger/older sibling" then the probability would shift.
That’s precisely what I was thinking. Age plays absolutely no relevance here.
No, but the fact that boy/girl families are twice as common as girl/girl families is very relevant. Showing that through the older/younger chart was an easy way to help people wrap their heads around the concept, but your right, age doesn't matter. The math still checks out, though.
An easy way to check this is two flip two coins, over and over again. You'll find that about half the time you get one head and one tail, but only a quarter of the time will you get two heads, making the mixed tosses twice as likely as the matched toss you're looking for.
Edit: Made a follow up video with an explanation saying mostly the same things I say in the paragraphs below - th-cam.com/video/ElB350w8iJo/w-d-xo.html
Okay if you haven't watched the video yet (and have never seen this paradox), then don't read the following paragraphs just yet. Look at the math I show and see what conclusions you can come to. After A LOT of thought I see some issues but they are very subtle and not obvious....well they weren't to me, but I want to try and clear everything up below.
TLDR: The fact some GG parents who have a daughter named Julie won't tell you about Julie but rather the other daughter matters here. So if we only know that the people in some room have 2 kids, then when one tells us they have a daughter, the probability is 50%, when they mention the name, it stays 50%. If instead we know everyone has 2 kids and at least one daughter (this is known before talking to anyone) then the probabilities all are 33.3%.
Longer Version: So first I think all the math in this video holds and is perfectly accurate IF we treat this more like a typical probability problem and phrase it like this. "If we have a room full of people who have two children then ask those with at least one daughter to step forward, what is the probability a randomly selected one has 2 daughters?" This answer is 33.3% as stated in the video. If you then ask all of those people who have a daughter named Julie to step forward then 50% of those families will have 2 daughters, also as stated in the video (because you have twice as many potential Julie's in each (girl, girl) family). And lastly if instead of the name we ask those with a daughter who was born on a Tuesday to step forward, then 13/27 of those will have two daughters. All of that is correct and although it may seem kind of weird, I wouldn't call those paradoxes.
However, in any stats class when we are GIVEN something, we rarely think about HOW we are given that information and in this problem we need to. Imagine a room of 7500 fathers who have 2 children, one of which is a girl (that means 5000 will have a son and daughter, while 2500 of them have 2 daughters). Then let's say you talk to every single father in that room and at some point in conversation they all end up randomly mentioning the name of one of their daughters (or their only daughter if it's a GB/BG family). If 1/100 girls are named Julie, then 500 fathers with a son and daughter will have told you Julie (which is every BG/GB father in that room who has a daughter named Julie as there's no other daughter for them to name). Then of the GG families there WILL be 500 fathers with a daughter named Julie as I stated in the video, assuming no overlap. However, only half of them will tell you of Julie, the other half will tell you of their other daughter. That means you've heard the name Julie from 250 GG fathers that night and 500 GB/BG families. If every single time you heard the name Julie you bet $1 they have 2 daughters, you'd win $250 but lose $500 and thus end at a loss. You'd only win 33.3% of the time which keeps the same probability as BEFORE we heard the name. This here kind of resolves the paradox I mentioned in the video with the whole "i have a daughter....whose name is Julie" part. The thing to note is that some of those GG fathers with a daughter named Julie will not tell you about her but rather the other daughter. So you're not HEARING about Julie from the GG families enough for it to be 50% and this reflects reality more of talking to someone in a bar who states the name of their daughter.
And actually you could argue there's a flaw in the previous paragraph because of HOW we obtain the fact that the father has at least one daughter. Imagine we are in a room full of 1000 fathers that have 2 kids but we DON'T know they all have at least one daughter (250BB, 500GB/BG, and 250GG). We then talk to all of them and throughout the conversation they all mention the gender of one of their children at random. That leaves 250 fathers with a boy and girl (half of the total) that told you they have a daughter and 250 fathers with two daughters (all of them) who said the same thing (since that was the only option for them). Because of this you have a 50% chance of guessing correctly that they have 2 daughters. If those fathers then tell you the name of one of their daughters and you analyze all who say Julie (or any name for that matter) you retain that 50% probability.
To summarize, it's all about whether you know something about all the parents in that room vs what they tell you at random during conversation. When you to a bar full of strangers, since you don't know anything about the people there in terms of how many kids they have, you could say the 50% stays consistent in this video. But if we know the parents in that room have 2 kids, one is a girl, you get the 33.3% in every situation. And if you know everyone in that room also has a daughter named Julie, then you go to the 50%.
Agreed. Just one small caveat regarding the last sentence. It's not just that you know that everyone in the room has a daughter names Julie that enables you to say that the other sibling is a girl with 50% probability. It's rather the fact that they have been selected from a random population of two-children families (with randomly assigned genders) on the basis of the selection criterion that one sibling is named Julie. If you had rather selected them on the condition that the younger sibling is named Julie, then you would still know that everyone in the room has a daughter named Julie but, in that case, the probability that the other sibling is a girl would be 1/3.
...and that's because, in the later scenario, we would have effectively discarded from the population under consideration all the families in which it's the older older sibling who is named Julie.
I'm going as far as to say that the math presented in the video is plainly wrong, because you're mixing up implicit assumptions that are never mentioned. The mathematical analysis you have made in the extra pinned comment is completely correct and essential for understanding this seemingly 'paradox', but the main video suggest something completely different that is just incorrect and probably very confusing for many viewers.
In the video, you act as if just hearing the parent in the bar say the name Julie changes the probability from 33% to 50%. This is NOT the case. As you explain in the pinned comment, the probability only changes if you ask all parents with a child named Julie to step forward. In this way, you are sure that 100% of the parents with two daughters, one of which is called Julie, step forward. However, if the parent in the bar just gives you a random name of a daughter, only in 50% of the cases of a parent with two daughters, one of which is called Julie, they will say the name Julie and 50% of the time the other name. You can do your whole analysis again and see that the probability is still 33%.
In the same way, one can see that in all cases in the video where you claim that a probability 'suddenly and counterintuitively' changes when we get extra information, this is not really the case in the setup in which you explain the paradox. The main reason the story sounds paradoxical is because it is WRONG, not because it is complicated.
I hope you could emphasize more in the first line of the video description that probability theory is not actually so paradoxical as you describe it to be. I would highly appreciate it if you coud include something like "WARNING: this video is made under a wrong conception of the paradox and the math behind it. Please read the pinned comment for the correct mathematical analysis." It would be a shame if after this video people think they have learnt something about how probabilities work, but what they have learnt is actually false. Thanks in advance!
@@bastiaanabcde I agree that the video is misleading, but I am also impressed how very fast after posting it MajorPrep rethought the problem completely through and arrived at a correct conception. That's not something that you see very often on the Internet. I am fairly sure he's going to either make a followup video or edit in some caveat in the way you are suggesting.
@@pokerandphilosophy8328 Yes, I was also very happy to see this mathematical analysis, and indeed for internet standards this is surprisingly correct. So well done MajorPrep! Now let's make sure the viewers actually get aware of this haha.
In your first point at 1:20 when claiming that there is a 33% chance of the other sibling being a girl, there is a really big problem with how you are presenting the case. When comparing the known girl to the the potential boy, you state the possibilities as *girl born first - boy born second* or *boy born first - girl born second.* But when comparing the known girl to the potential girl, you just say "and two girls." But in the case of a comparison of the known girl with the potential girl, one of them still must be born first and the other must be born second, and there are two equally likely orders in which this can happen, giving this scenario two outcomes to compare against the two outcomes of the boy-girl/girl-boy pairs.
The problem arises because you are selectively identifying the known girl. When comparing her to the potential boy, you give her the identity of "older/first" or "younger/second," aka order-of-birth. However, you fail to preserve that order-of-birth identity when comparing the known girl to the potential girl. If you were consistent in the way you analyze the outcomes, you would see that the probability is *always* a 50% chance of the other child being a girl because the known girl would still have to be "older/first" or "younger/second". You can see this in your second argument when you use a name as an identifier rather than order-of-birth. By not remaining consistent in the first argument, you're ruining the integrity of the comparison.
@paula You either did not understand the video or did not understand my reply
this problem somehow reminds me of the 3 doors thing
where there is a game
and there are 3 doors and you choose one
the game master opens a door that would be a fail
and then you can change your mind to the other door or keep your first choice and you should always change the choice cause the first time picking it was 2/3 chance to fail and now it would be more probably to change
or something like that
I’m having problems understanding why the fuck it matters what order they were born in....
@@lusmn268 Ah yeah the Monty Hall problem probability question. Numberphile has a good video about that (th-cam.com/video/4Lb-6rxZxx0/w-d-xo.html).
so correct like
Her name is "Born on a Tuesday" - you're screwed
WAS, she is dead
I think the intuitiveness comes more readily when you just think of it as "the math changes when you are liking at it from the perspective of the identified daughter", whether it be that she's identified by her name, day she was born, etc.
So what I'm getting from this is that if I want to increase the likelihood of having two daughters I just have to give the first one a name? Sick
Okay, I checked and this was published 7 April. But maybe it was *filmed* on the first?
lol
Yeah...I really don't want this to be the case
And they say that dope is harmless :-D
I wish it was, but frankly, I had an exam with harder shit than this... yeah, it's weird, but probabilities get a lot weirder still, with pretty... complicated stuff that one would not even dare use intuition for, simply because most of the time you need 10 hours to understand the problem anyway...
Gary Payton named both of his sons Gary Payton Jr. Your math is off. QED
Greatest perimeter defender of all time.
George Foreman named all 5 of his sons George.
actually it is not...
math is a very precise thing, even those bits that seem random, like rolling a die.
it is a condition that just one girl is named Julia.
if both kids could have the same name... well.. the probability of both kids being girls would be 3/5
This plus that certain names are significantly more popular in older time periods meaning it may be a well known name such as cleopatra
I was doing a search for some girl/girl and somehow ended up on this video.
I was just looking for Julie/Julie.
May made my day. Thank you gentleman.
You wont find in this ...tube
But what is the probability that you found some girl/girl action?
Probability of his step-daughter also named Julie?
this reminds me of how in quantum physics, once you make a meassurement it collapses the wave function, just like labeling a girl a certain way changes the probability
Man: I have 2 children one of wich is a girl born on a Tuesday, her name is julie, she's standing next to me, is left handed and wears glasses.
What is the probability of that family having a dog?
8
The ambiguity here is easier to spot if you reformulate this as questions and answers.
Q: Do you have at least one daughter?
A: Yes, and incidentally the name of the daughter I am thinking of is Julie
Then the probability is 1/3
Q: Do you have a daughter named Julie?
A: Yes
Then the probability is 1/2
yes exactly. There is only a "paradox" because the problem is formulated in an ambiguous way. If you would ask everyone
"Do you have at least one daughter, give me a name of one daughter
and they answer:
"I have at least one daughter, her name is Julie".
The probability is *drumroll* still 1/3. A simple symmetry argument suffices. But what may confuse some people is that they forget the fact, that only 1/2 of those that have two daughters, one named Julie, will actually give you the name Julie. 1/2 of the people that have exactly two daughters, will tell you the name of the other daughter
The name doesn't actually make it 50 50 in that scenario. There'd be some overlap. Or chance of overlap. I'm not sure the math. But let's say we now have 50 b/g families with a Julie. And 50 b/g families with a Sarah. However there'd be 98 or 99 families with a Sarah and a Julie. Even if it's 99.9 families. It's still overlap. This is the same logic as his birthday Tuesday math
yes, this way. the video is flawed as it puts both cases in the same basket
@@qwertz12345654321 The question posed by the video has the parent stating that she has at least one daughter, so theoretically, in the GB/BG cases there's a 1/2 chance of saying she has at least one son. Does that mean there is a difference between you asking if someone has a daughter, and them simply stating it? I would say yes, because if you ask all 2-child parents if they have a daughter, 75% will answer 'yes', but if you ask them all to state the gender of one of their children, only 50% will answer 'girl'.
@@MatthewJensen77 yes definitely. It is very important to closely observe the information you are given, which doesn't always have a intuitive interpretaton.
Doing maths on language will only reveal the vagaries of language :D
what is vagaries? Did you mean ambiguity?
Waffle Basket vagaries means something more like unpredictable change.
MortenStampe vagueries*
Koray Acar also sometimes spelt fegaries.
@@peterdunlop7178 i thought it was derived from 'vague', but whatever works i guess
Someone contact Presh talwalkar
F54DF4 A044 Please. I want to see him debunk this, as it’s wrong.
@@danieledgmon4260 it's not wrong. In fact he talked about a very similar thing
@@danieledgmon4260 th-cam.com/video/go3xtDdsNQM/w-d-xo.html
@@danieledgmon4260 I emailed him asking him to debunk this
@Hunter K , didn't you see the attached link? He has a video with pretty much the exact same conclusions.
Oh I understand now! Adding the name is switching the question from "If I have 2 kids and one is a girl, what are the odds of the other being a girl?" to "Given I have 2 kids, and I have a girl X, what are the odds of X's sibling being a girl?"
Congratulations. You understood something wrong
@@samilaliyev590 Um, no, he understood it lol
@@samilaliyev590 There is child A and child B, once we know the name of one, we are talking about 1 particular child and not either A or B
@@jamescarmichael8969 still, nope
@@samilaliyev590 its clear you have no idea
The problem with this is cherry picking the distinction between the girls. He's deciding that when you dont have an identifier (g1, g2) is the same as (g2, g1) which in statistics is already incredibly wrong. Even without given identifiers you must always count both versions of two girls as separate, distinct, and plausible outcomes.
“I have 2 children, one of which is rolling down in the deep”
“What is the radius of Jupiter’s moons combined?”
But (and correct me if I'm wrong) if we take in account the birth position (boy first born or second born) to split the B/G probability, then we should double the G/G too. That girl might be the first or the second too. It would double the B/B probability too, but that's not taken in account as we said that one of them is a girl.
So:
1. (B/G)
2. (G/B)
3. (G1/G2)
4. (G2/G1)
100/4 = 25 \\ 25*2 = 50%
This is correct
So I just got halfway through and realised my head was hurting, but thought, “Hey, it’s okay, I’m halfway through - he’s still got half the video to make my head feel okay again”. Then he says “Okay, for anyone who’s still confused, it’s just gonna get worse from here”... Oh boy. 🙄🤔🤯
I know this removes a lot of the subtleties that make this video interesting, but I've finally found a way to understand it intuitively (I was borderline driven to insanity by this video when I found it about 6 months ago, and recently returned to it to try and understand it again!)
Just use coin flips:
"I flipped 2 coins, at least one of which was heads"- 2 heads would be a 1 in 3 chance, as you could have head tails, tails heads or heads heads. There's a 1/4 chance of getting heads twice, but we're removing 1 of the 4 possibilities by excluding the tails tails result.
"I flipped 2 coins, at least one of which was heads, and that one was the bigger one/rustier one/fell off the table", now it's 50/50, because you only need to work out the probability of the other coin being heads as well.
Idk why that is so clear to me and the son/daughter situation nearly broke me as a man, but at least now I get it 🤣
Please make a video experimentally testing this! Somehow arrange enough volunteers to fill an adequate sample size of parents who have two kids, and create scenarios with the very particular wording you've described.
This is really, really dependent on how the information is generated. If you ask a couple, "Do you by any chance have a daughter named Julie?" and they say yes, you get a very different distribution than if you first ascertain that they have at least one daughter, then ask the name of one and find out it's Julie.
Even though you possess the same facts about the couple and their daughters in both examples, the implied distribution is different.
Correct. In a world where all girls are named Julie, nothing changes. By considering only girls named Julie the size of the sample set (Families with a daughter named Julie) is greatly reduced by the more limiting condition. You are being asked to calculate a DIFFERENT probability. Adding additional information only changes the problem if you are asked to calculate a DIFFERENT probability. Going back to simplest most basic definition of probablility (P=positive examples/all examples), either the numerator or the denominator (or both) must be changed by the additional information to yield a different result. In any problem there are several probabilities that can be considered or requested and it is important to be be very precise about what is being asked.
@@Rick_MacKenzie Exactly. The paradox is all about subtly switching what probability is being asked for.
the apparent paradox has nothing to do with switching what probability is being asked for. the apparent paradox comes from splitting the cases where the sibling is a boy into 2 groups depending on whether the boy was born first or second. it doesn't matter which child is oldest, there are only 2 options; the sibling is either male or female which is a 50% probability.
If I met a guy in a bar and he told me that he had 2 kids and one was a girl the real probability that the other was a girl is 0%.
Why? Because nobody would say I have 2 kids and one of them is a girl, the other one is a mystery. If they were both girls he wouldn't say one is a girl.. Oh and hey, so is the other one.. 😂😂
0% is the correct answer in the given scenario. 😜
It's 2019... I think there is a greater than 0% chance that someone somewhere would treat their child's gender as a mystery, because they haven't decided what they identify as yet. LOL!
It's not saying that the other child is a mystery, rather they only specified the one and not the other
there is a difference in saying at least one of them is a girl and one of them is a girl
@@NinjarioPicmin but if the person said something like "my daughter, Julie" then that leaves it open to having another daughter with another name or a son with another name. The wording of the puzzle is for clarification
@@jebadia4518 finds it important to conduct life without regard to irony or humor. Statistically there is a one in thirty four chance that he is a three toed sloth.
I don't understand how seeing the daughter increases the probability to 50%, because, let's assume the daughter isn't like a infant (which would signify that that her sibling is automatically older) but she looks about 10, this means her sibling could be older or younger than her. So the probability is now boy born first and girl born second, girl born first and boy born second, or girl and girl.... this would keep the probability at 1/3...
It's the same situation as the Julie example. If a person has two daughters, then it's twice as likely that you'll see one of their daughters vs if they only have one daughter. Thus, it increases the probability of having two daughters from 1/3 to 1/2
If you flipped two coins, but you dropped one and couldn't read it-- and you looked at the coin you still had and it was tails-- would you be able to then say that there is a 67% chance that the other coin is therefore heads? Because that is what you are suggesting.
@@TheHobgoblyn No, because there you only know that the first coin is tails. That's different from knowing if at least one coin is tails. Knowing that the first coin is tails eliminates 2 of the 4 possibilities, but knowing that at least one coin is tails eliminates only 1 of the 4 possibilities.
@@kaushalmaganti8839 aight I get it now
I don't really know if I actually understand exactly how this works, but I will try to answer your question anyways:
We do not care about their age. Let's say that we call the first child A and the second B. There are four equally likely possibilities:
1: A and B are both boys.
2: A is girl and B is boy
3: A is boy and B is girl
4: A and B are both girls
If you observe a child, you know the gender of one of the childs, let's say A. Therefore, option 3 can not be true (as we know A isn't boy). No matter whether we observe the child or not, one of them are always called A and the other is always called B. We can not say that option 3 can also be true, as we might had actually saw child B. They have one name only and always. To understand this, imagine that they have a sign on them reading their name. You observe on of them and you see that it is a girl. You can also read her name, and thus you know what the girl is called. She can't "actually" be called something else, as you can easily read her name on the sign.
You changed the problem subtly by introducing birth order. That wasn’t the original question.
If we have two dice, black and white, and have someone roll them and say “at least one gave six” you have 6x6 grid of possibilities with right-down sides of it as suitable ones, only one of them has other also as 6, so probability of ✨other✨ being six is 1/11.
When you hear “black rolled six” /“white rolled six”, you have only right side or down side of suitable possibilities, so 6 elements, and probability of ✨other✨ being six is 1/6.
The paradox is in word ✨other✨. In first sentence this word means any of two cubes, while in second it mean one particular cube. That’s where the gap is hidden, as I think - more of a linguistically paradox, like “father punched son because he was drunk”
To an advanced alien race millions of years ahead of us, where relativity and quantum mechanics are taught in kindergarten... This problem *might* make intuitive sense 😂🤣
I think I see the problems here...
First, if you flipped 2 coins at the same time, and someone hid one of the two coins from you and the coin you could still see was heads, you wouldn't be able to say that there is a 67% chance that the hidden coin was tails. The hidden coin still has a 50/50 chance regardless of the result of the coin you see.
Second, your example of people in a conversation-- if a person has 2 children and 1 is a girl AND they mention one of their children at random and the child they mention is the girl, then there is a 50% chance that the other is a girl. Because although there might be twice as many families with 1 boy and 1 girl than there are families that have 2 girls, there is double the chance that if a random child is mentioned in the family with 2 girls that the child mentioned will be a girl.
Therefore, in your example of someone saying "I have 2 children, and 1 is a girl"-- the chance of the other being a girl already becomes 50%. Also, if you have a random girl with 1 sibling, then the chances that she has an older brother or older sister or a younger brother or younger sister are all equal.
The probability chart does suggest that if you went up to a random person and asked "Do you have two children?" and they said "yes" and then you asked "Is at least one of them a daughter?" and they said "yes", then the chances that they would have 1 boy too would be double the chances they had 2 girls.
But at the same time if one were to poll the girls in a class of children who have 1 sibling whether their sibling is a boy or a girl, the numbers would be equal because there is double the chance that the older sister or younger sister is in the class.
After flipping the two coins, you fixed one to be revealed. This is the same as naming one of the daughters, or naming a coin (left or right) to be revealed.
If you flipped two coins behind my back and told me at least one was heads, it could be the left, or the right, or both. There are 3 equally likely cases, 1 of which includes two heads.
Thanks dude. I couldn't find a way to make sense of how one girl could alter the probability of the other being a girl, but now I get it.
Almost but there's a total 4 possibillities. We can call the coin you Are talking about coin x om this example. 1 Coin x is heads and coin B is tails. 2 Coin B is heads and coin x is tails. 3 Coin x is heads and coin B is heads or 4 Coin B is heads and coin x is heads. Therefore the the probability is 50%. I understabd what they Are trying to. But not halling the one Coin ore om the video the girl anything, doesnt mean that the girl cant be either the First or second girl/Coin. Thats just nonsensical.
@@jonhmm160 Your spelling is nonsensical
@@AnalyticalReckoner ehehe that's true:P. Sorry i'm writing this on the Phone and is also not great at spelling.
The 33.3% is clearly wrong. The original question in no way requires the ordering of the pairs (in terms of who was born first). That was erroneously added to the conclusion. Even if you include it, there are 4 ordered pairs - (girl first, boy second), (boy first, girl second), (girl A first, girl B second), (girl B first, girl A second). The percentage is always 50%.
Thanks Josh. Was looking through for someone putting it concisely to save me doing it myself.
yes and if i may be so bold... your 1st and last sentence are all you really need cuz that is the purest truth... "The 33.3% is clearly wrong. The percentage is always 50%."
I believe you are mistaken since you effectively double the probability of 'girl A' or 'girl B' being born first. The first child born only ever has a 50% chance of being a girl, and so if you split that chance between 'girl A' and 'girl B' you would have to attribute 25% to each of them, not 50%. Once you do this you arrive at a probability of 33%. This is similar to rolling double sixes with a pair of die where obviously there is only 1/36 chance, not 2/36.
@Josh Reif Yes the ordering doesn't matter before we have the name (or some other specific identifier, like seeing her in person as was also talked about in the video). And therefore it is -a 50/50- ~33.3%.
But as soon as we do get the name, the ordering will matter for the double girl side, but not for the case of the boy being her sibling. This is why it changes to -a ~33.3%- 50%
EDIT: Got my numbers mixed around, in the hurry, reasoning is still correct though
@@GummieI Why does the name matter who is born first? It never matters. And the video still says the opposite of what you're saying. From start to finish, the percentage is always 50%
I think the most intuitive way to understand this is the following:
It doesn't make a difference whether Julie is the older child or the younger child.
Thus let's assume that Julie is the older child (without loss of generality).
Now the question is given that the older one is a daughter named Julie, what's the probability that the younger one is a daughter?
Now it's clear that the older child doesn't affect the younger child in any way thus the probability of the younger being a daughter is 50%.
the question states "at least one of which is a girl". GB and BG can be grouped together as its own option, since in both scenarions one of the children is a girl. there are 2 options and its 50/50.
I think I get it it. It's about how u word it. For the first one, what it is the chance that the other sibling is a girl given that one is a girl.
The equally likely options are:
girl that is being talked about, boy.
boy, girl being talked about.
girl being talked about, another girl.
and another girl, girl being talked about.
so it's 50 50
This is the correct answer. Another way to think about it is that if someone has a son and a daughter, they have a 50-50 chance of saying either "I have at least one son" or "I have at least one daughter", so this increases the probability that the other child is a daughter back to 50%. The paradox is that the probability of a person saying a statement is not the probability that the statement is true.
@@kaushalmaganti8839 hmm let me think about that
Actually, saying I have atleast one daughter consideres and gives information about multiple daughters and I have a daughter named Julie gives no info at all about the other daughter.
Similarly, the actual is the same but saying one of which was born on a tuesday gives information combined of one or two daughters and not just a single one.
It is when the info given can be attributed to more than one person in calculation is when we get different values.
@@MdSheraj ye, asalamu alykum btw
@@meeharbin4205 wallikum asalam. I'm made a blog post about this too. You can check it at blog.mdsheraj.com
Them: "I have two children, at least one of whom is a girl" *who says that, by the way?*
Me: "What's her name?"
Them: "Julie"
Me: "Congratulations, 1/6th of your sons just turned into girls."
Something wrong with that paradox. Any random information cannot change the probability. When you know the name the only thihg that has been changed that you know it couldn't be the second one with that name. I am not convinced
Variable change
Movie 21, Ben Campbell scene
@@harshalranjane7669 that's not what that scene about. If you chose that i have pr. 1/3 that i have two daugherts, and after your decision i say "The name of the second child starts with the letter B" you'd better change your decision, because we have new information
K, cool
Edit: Actually hol' up , when did this question about sex of someone's child get related to age?
Wouldn't (B,G) and (G,B) set be considered same if age wasn't a variable considered?
Edit 2: nvm he stated the question wrong
I don't know if that will help you but see things that way :
If I tell you I have a two children and at least a daughter and then you ask me if I have a daughter born a monday
If I have two daughter the probabiliti that I answer yes is two time bigger than if I had only one girl
The information is random but what is interesting is that it exists ( if I have only one daughter it only exist one day where one of my daughter was born whereas if I have two daughter,there are two).
sorry for my english :)
@@matteo7123 everithing you said is right. Except the fact it make nothihg to do with the video :D Actually, I found what he did. He mixed up families and girls. When the guy says he has a girl, we decide in wich family he is, with two girls or a girl and a boy. But in this video he transforms it into the situation, when we picked a random girl and trying to find out has she a sister or a brother. And of course it will be 50% chance she has a sister
The problem with your first scenario answer is that nowhere did the question ask anything about birth order. Therefore, the answer is 50/50. You are reading into the question.
There is a subtle error in the video. If you know the other guy has 2 children, and you ask him "Do you have a daughter named Julie?" Then indeed, 50% of the people answering "yes" will have two daughters.
However, if every family with at least one daughter makes exactly one statement "I have at least one daughter named X" and families with two daughters randomly select one of their daughter's names for X, then the chance for two daughters is only 33%.
The case in the video is closer to the second scenario.
When you don’t get sleep for 3 days straight...
W R O N G
"I have two children, at least one of which is a girl"
Order 1) Girl + Unknown
Order 2) Unknown + Girl
The unknown is either a boy or a girl. So...
Order 1.a) Girl + Girl
Order 1.b) Girl + Boy
Order 2.a) Girl + Girl
Order 2.b) Boy + Girl
Both 1.a and 2.b have the same outcome: Girl + Girl.
*>>>>>>>>>>> HOWEVER, THEY DO NOT CANCEL EACH OTHER OUT.
Wrong idiot
Only if you account for the other pairings now possible with this second female gender you've now created to "fix" the problem... that's gunna get messy
true... zack is literally shifting the focus of the analysis from the "girl" to the "family"
I hope this explanation helps simplify things for anyone confused here...
When you say, "Out of two children I have, at least one is a girl, and she has (insert any trait here, we'll call it "X")." , you're not giving two statements but rather three, that being:
Statement 1: At least one of your children is a girl.
Statement 2: One of your children has trait "X"
Statement 3: (Most importantly) Child with trait "X" is a girl.
If you have said, "At least one of my two children is a girl. One of my children has trait "X"."
It would be like the first sentence, only difference is that Statement 3 isn't included here. And this what most people think when they say, "Why would a random trait affect the probability regarding their genders, they're unrelated!"
However, with the sentence in question here, because Statement 3 is implied with the words, " and she has trait "X"...", a direct association between the child's gender and trait "X" has been made. This then allows trait "X" to be a relevant factor even if the question was about gender, because Statement 3 links the two together. Had Statement 3 not been made, trait "X" would be irrelevant.
Clever
You explanation makes sense and easy to understand. Thank you.
Absolutely true. The real key to the "trick" is the phrase stating that "at least one is a girl", which never identifies which child is associated with that trait (gender) and thus there are still 3 possibilities. The moment they link that trait (e.g. "my oldest child is a girl", or "the girl is named Julie", or any other possible linkage) then the possibilities drop to only 2.
This seems more like an english grammar puzzle than anything.
It's only counterintuitive because the question is based on a false assumption.
I've seen this done many times - the question is framed wrongly. You ask "What is the probability that the other child is a girl?" This question implicitly is based on the assumption that beforehand, we were talking about one specific child out of the two, or else "the other" wouldn't make sense if we weren't talking about "one of them" before - which we weren't! So using that phrase means the question is based on a false assumption. This is exactly where the counterintuitivity arises. Correctly, the question should be "What is the probability that both of them are girls?", which is less counterintuitive.
If someone says "I have 2 children, at least one of which is a girl" to you, just smile and walk away slowly without turning your back, because who actually talks like that outside of math and logic problems.
Tzisorey Tigerwuf someone who ends an interrogative sentence fragment with a period instead of question mark?
@@HighestRank
@@tzisorey *facepalm* Did you just call yourself _his_ ?
The given method seems to base its numbers off looking for the number of Julies in each group and finding 250 in the boy&girl group and 250 in the 2 girl group. This doesn't make sense because if the parent has two girls and gives one name, they would have to choose one or the other and can be assumed to choose at random. Of all the two girl groups with name Julie, the parents would only be expected to choose Julie's name to give 50% of the time and thus only 250/500 2 girl groups with a Julie would say Julie, compared to the 500 Julies in groups with one girl whose name would be stated every time. The 50/50 probability is incorrectly double counting the number of Julies that would be mentioned in the 2 girl groups, because one of the two is randomly selected. Therefore I believe the probablity in fact never changed, remaining 33.3%.
exactly what i thought!
That's not how children's names are chosen. Your model isn't correct because nobody starts off with two children and decide which one to name Julie. What actually happens is, they have a first daughter, where 25 people will decide to name her Julie, just like those who have 1 girl followed by 1 boy. Then they have a second daughter, where 25 additional people will decide to name her Julie, just like those who had a boy first then a girl. That makes a total of 50 families who would name one of their daughters Julie.
@@letao12 I believe that Trey B is referring to "giving a name" as the guy at the bar telling you the name of one of his daughters, not how the names of daughters are actually decided at birth.
Ah I see, sorry I misunderstood.
In that case the other 50% where the guy doesn't name Julie is irrelevant to the problem. Basically we want the conditional probability of 2 girls given that the guy has already named Julie. Naming Julie is a prior condition. The chance that they don't name Julie is excluded by the prior.
Okay I like the analysis but have a follow up. Let' assume half of the girls out there are named Julie. Now given 2 families, each with 2 girls, wouldn't we expect both of them to have a daughter named Julie (since you'd take half of 4 to get 2 girls, then assuming no overlap that means 2 families)? But your analysis would assume only half those FAMILIES would have a daughter named Julie, which means there'd be 1 Julie out of 4 girls, which goes against our initial probabilities.
Anyone else who checked if this was an April fools prank?
I went to an abstract bar and tested it (try running it yourself, it's javascript):
// boy and girl tally
var bNg = 0;
// 2 girls tally
var gNg = 0;
// sample size
var sample = 1000;
// loops through sample
for(let i=0; i
The For loop would indeed have been easier to code.
Julie: "Did you just assume my gender?"
As I see it, there are two distinct situations.
first which he says: 'I have a girl named Julie'
two which he says: 'I have a girl, her name is Julie'
(in both of them he says: 'I have two children')
In the first one: the logic of the 50% works, because you learn of a girl named Julie.
In the secon: the 'name information' is pointless, as it is given as information about the daughter. Information which she obviously has.
4:04 actually you assumed families can name both their daughters Julie when you made it 5000 girls in total, if 50 of them are named Julie there are 50 other girls that cannot be named Julie (their sisters) which you didn't take into account at all.
If you make an assumption it should be made before the calculation, not somewhere in the middle
A question: We know from Nash that there is always an optimal in a Nash equilibrium. But can we always find it?
We literally went over this in class about a month ago. Was weird to understand at first.
This is the Monty Hall Problem repackaged. The "paradox" is that you're shifting from an unconditional to a conditional probability without stating it outright.
Came here to say just this. I was surprised I had to scroll down so far to find it.
"I have a daughter named Julie." Only restores the parity if there was something special about the name Julie which prompts the respondent to consider the names of both his/her daughters. If he was asked to randomly select one of his daughters and then confirm if that selected daughter's name is Julie he might answer "no" if he has two daughters, one of whom is named Julie, but it isn't the one he selected.
I believe you are wrong. I think there are 2 ways of arranging the girls before one of them is named, such that the chance is always 50%.
Constantinople, 1054 I thought this too
But before a characteristic is defined, the equation has no means of distinguishing the different possibilities.
0:36 I paused the video to check out the pinned comment, but it seems to have been removed. My life is a lie.
I'm throwing the 'shanagans' flag on this play.
The names and birth order are irrelevant to the core question, "what is the probability of my other child being female?"
All the extra information in the world does nothing to change an isolated variable. It doesn't matter that given girl likes liver flavored ice cream and has a crush on Chris-Chan.
The reason everyone fights over this is because the question is worded such that it is deliberately vague and without absolute reference frames.
TL:DR - doesn't matter how she's a special snowflake, it's still 50/50 (Or 52/48 if you want to be technical about it).
The probability is 50% no matter once. Naming the daughter only dignifies her as a separate person in our brain. When we are told that he has one daughter, even thought a name is not given, we can label this daughter daughter 1. There fore there are these possible cases: daughter 1 + son/ son +daughter 1/ daughter 1 +daughter 2/ daughter 2 +daughter 1. This makes a 50% chance. The paradox only roots from a cognitive bias of labels in our brain. Though we do not naturally label someone if we are not given their name, they should still be dignified. If we simply label them both girl there is nothing showing the difference, therefor we ignore an entire possibility.
(Sorry for my bad Englisch)
What you do is: You change the perspective of probability. I give You an example. When You give the girl a Name, You calculate the probability if a that Girl have a sibling wich is a girl or an boy. The same ist with a weekday, or day in moth, You always change the perspective, and that matters for the calculation. You know that, I guess.
Really nice video.
I believe there is a slight mistake in the video. Zach Star, please correct me if I am wrong but it would be helpful as I'm doing Further Maths this year! Basically, I think the mistake is in the question. If you say you have a daughter and she is, in scenario 1, the younger of the 2 siblings, then the other child can only be a boy or a girl, meaning the probability of the other child being a girl is 50%. In scenario 2, if the girl is the older sibling, the younger sibling can STILL only be a boy or a girl. Sometimes, if you have the pair A and B, that is considered to be the same pair as B and A. So why does it not apply to the concept whether a boy is born before a girl? What I mean is, if we label the pair of children/siblings B (boy) and G (girl), then wouldn't the pair B&G be the same as G&B, leading the 2 out of 3 options to cancel out to one out of 2?
I totally agree with you, the introduction of order of birth in the answer is falsing the result.
This is probably really late, but essentially what we don't know is influencing the results.
Say we flip 2 coins. there is a 50% chance coin 1 lands on heads, and a 50% chance coin 2 lands on heads.
The probability that both coins land on heads is 25% (50%*50%). Easy so far.
The options for what we can get are currently:
a. Coin 1: heads, Coin: 2: heads
b. Coin 1: heads, Coin 2: tails
c. Coin 1: tails, Coin 2: heads
d. Coin 1: tail, Coin 2: tails
In the example in the video, we can substitute heads for boys and tails for girls, firstborn for coin 1 and second child for coin two.
It's now:
a. firstborn: boy, secondborn: boy
b. firstborn: boy, secondborn: girl
c. firstborn: girl, secondborn: boy
d. firstborn: girl, secondborn: girl
We can now cross off the option of both boys, as we know at least 1 is a girl.
-a. firstborn: boy, secondborn: boy-
b. firstborn: boy, secondborn: girl
c. firstborn: girl, secondborn: boy
d. firstborn: girl, secondborn: girl
alas, we can see that exactly 1 option is both girls.
Essentially what is happening, is that x, y and y, x are different things, because they each have their own probability of happening. (25% for both boys included, 33% if not.)
I hope this helps.
@@SnowRose-wn6gj This whole video is utter nonsense. It's like the wrong solution to the monty hall paradox. The first child has already been revealed. The original set of outcomes and combinations no longer matter, only the new set of possible outcomes with the information revealed. Which means it's 50/50 always in every example.
Not only this is counter intuitive, it's wrong. The order of birth, doesn't influence the result of your initial question.
This is just gimnastic to get views on youtube. SAD.
I'm reminded of the 10,000 people, including nearly 1,000 with PHds, who wrote letters to tell Maryland vos Savant that her solution to the Monty Hall problem was incorrect despite her being demonstrably correct. SAD.
Where’s the pinned comment. I would like to know what else he was going to say in the intro
The real answer relies in WHO asked you the question. In 100 families, all with 2 kids, at least 1 of which is female, 33 families will have a second female. If a parent asked you, assuming there are the same number of parents in each family, the answer is 33%. You have run into a parent of one of these families that have 2 kids and at least one daughter and 33/100 of them have a second daughter. The odds the parent you ran into is a parent of a second daughter is 33%. However if one of the children tell you the riddle, it is either a 50% or 0% chance. If a girl in the family tells you the riddle, it is 50%. There are 150 girls in this scenario and 75 of them have sisters. So there's a 50% chance you ran into a girl with a sister. Obviously if you run into a son of the group, your chance is 0%, because he isn't a girl. Now if you ran into BOTH the parent and daughter of the same family, you can fall back to the "family" stat of 33% because although for any given girl the number is 50%, you ran into a parent. And for any parent, the 1st girl was already a given. It's not really different probabilities of a second girl existing. The same number of girls exist the whole time. The probability is that of who did you run into? In other words, in a family of 1b,1g, there are 2 parents to 1 girl. In a family of 2g, there are 2 parents to 2 girls. The 2nd girl exists half the time, but the existence of the girl does not magically add more parents for you to run into to ask you the question.
I came up with exactly this seemingly paradox myself and I felt really proud when I did.
It really comes naturally when you do the maths, because the only reason that the probability is 1/3 is because there is nothing that allow you to tell one child apart from the other. It’s basically 2 random variables X and Y but no idea who’s X and who’s Y.
So I thought, if the father add « Her name is Name » then you can have 2 random variables : X and Name, and you can tell them apart and the probability changes to 1/2.
In some kind of way, I feel like it ressemble quantum intrication : in the first situation, the information you have on the system is greater as a whole than within its parts.
The second problem is faulty, ‘Julie’ is a random value and could as well have been any other girls name.
This means the answer is still 1/3. Perhaps if the other 9900/10000 girls were all nameless this would work.
Even in the case where you ask if one of them is named Juliet, it still isn’t 1/2 if 1/100 of girls have that name.
The second child would have a 99/199 of being a girl as you remove the Juliet’s from the selection pool.
The math works, but only so well as Abbott and Costello's 7 X 13 = 28.
I somehow feel insulted.
The math works. AND THAT IS IT.
You just need to know the math...
@@Anthaghoull You're right, it does work, just like Abbot and Costello made 7 X 13 = 28. Watch the skit and you'll understand what I mean.
“I have two children, at least one of which is a girl.” What is the probability that the other child is a girl?
The birth order of the two children isn’t relevant information in that statement or the question, so the answer is 50%. It’s either a girl and a boy, or two girls.
It all depends on how the question is asked. If it instead it was: "You will have two children later in life, one of which will be a girl. What is the probability that the other child will be a girl?" Then yes, the answer is 33%, because there's four outcomes of Bb, Bg, Gg, Gb, and like you said, Bb can't be an answer.
But by stating one child is a girl before the question is asked, the probability becomes a simple coin toss to determine whether the other child is a girl. In other words, the two outcomes of Bg and Gb are the same thing if birth order is irrelevant.
You are right because the I in "I have two children" also give information. Making the order of birth on the two children not relevant. Shifting the analysis from global population statistics to "biological/binary permutation" (Probability of said person to have)
Yes you are right. As a multilingual person I can easily understand this while I see so many people in this comment section struggle.
Edit: I also want to say your example is brilliant.
no this is all wrong. imagine 4 couples with two children each Bb, Bg, Gg, Gb.
3 of these couples can correctly state “I have two children, at least one of which is a girl.”
but only 1 out of those 3 have two girls.
the probability works the same way given just that information for a random couple.
@@shiinondogewalker2809 But why imagine 4 couples when the first part says "I have two children" lol
Predicting the future birth order of two children (Bb, Bg, Gg, Gb) doesn't apply here because the question is in the present tense: "I have two children" rather than "I will have two children."
Basically, the difference between the present and future tense of this question is why the paradox exists.
Just because you read it in a book, doesn't mean it's correct. Same with what you read or see online.
This probability paradox is actually a way to understand quantum mechanics. Whether there is one girl or two girls represents the state of a particle, while giving the name of a girl represents observing a particle. Observation really does change probabilities.
With the first statement as you rightly said there are 3 possible options:
GB
BG
GG
=> P(G,G) = 1/3
However with the additional information => ".. whose name is 'X'", what is happening is identifying a specific individual in the "GG" possibility. This identification implicitly splits that as two possibilities => G'G and GG' : where G' is the girl with name 'X'
This will make the possibilities:
G'B
BG'
G'G
GG'
=> P(G'G | GG') = 2/4 = 50%
In a sense this identification is similar to saying "boy or girl" instead of saying "child". Specifying an identifiable attribute splits up the probability space.
But would this make an actual change if we were to ask a lot of people
- _ LIR _ - Yes. In fact, probabilities only really have an effect with large populations.
well unfortunatly it doesn't work like this. Look at the correction OP has pinned.
The error is right in the beginning, when the question is, "I have 2 children, at least one of which is a girl. What is the probability that the other is a girl?", we have 2 cases:
_Case 1_:- They are talking about the *child other than the girl*. In this case, since it has *ALREADY BEEN ESTABLISHED THEY ARE TALKING ABOUT THE GIRL*, the only possibilities of the combination is GG/GB, since there is *ONLY 1 SPOT TO FILL*, so the the probability is 50-50.
_Case 2_:- They are asking the probability of the second child being a girl, when *the first child is randomly picked*. In this case, we either choose a boy or a girl for the first outcome, but only a girl for the second one. So, the total outcomes are GG/GB/BG/BB, and we choose GG/BG, for a probability of 50% again.
TL;DR- The error arises in him considering only GG combination and not considering all of the outcomes, probability is 50% either way.
The error is in your reasoning. You need to watch the video again, since it explains exactly what you've got wrong.
I bet if I flip a coin 9 times and get tails all 9 times you'll still tell me the probability of the next flip is 50%. But what if i told you that the first coin had lincoln on it, does that change the probability?
Nope. But if I tell you nine of the ten flips were tails AFTER the tenth flip, it does change the probability ;p
You are just confused because we are using probability on humans in the video and mixing things up due to our intuitive language.
I clicked on the video thinking "If it's Monty hall problem I'll probably click off..."
Then I thought "Yup, Monty hall problem, but apparently there's more..."
Then I stay until the end and there was way more than the original Monty hall problem. Thanks for sharing this with us!
The answer is simple:
It's not 33% , the probabilty is 50% because:
There is 1 out of just 2 posibilities
1. gril and girl
2. boy and girl ( boy and girl or girl and boy is the same thing. it doesen't matter in this is case wich was born first, because that's another condition wich is not stated in the question )
3. boy and boy is not valid
I give you a simpler example with the same question
•From a store with only red and black cars I bought two cars, at least one of wich is red
• What is the probability that the other car is also red?
There is no paradox whatsoever. Its 1/2 no matter what. There is no "boy, girl; girl, boy; girl, girl". Its: boy, girl; girl, boy; girl, girl; girl, girl; because the two girls arent the same girl. And you dont have to know anything about the girls to know that. Its clear from the beginning and thats why intuitively people will say the probability is 1/2, which is correct. Not 1/3.
So if we had a group of 1000 2 child families and all those with two girls were asked to step forward, how many families would we expect to do so?
@@zachstar So your odds of having a boy or a girl at any given time are 50/50 but having two girls in a row is only 33%? I don't understand how naming or pointing at the girl changes that.
@Bo Dodge, no I'm saying if I ask you if you have at least one daughter and you say yes then I have a 33.3% you have 2 daughters (this wasn't what I said in the video but I've corrected it in the pinned comment and the follow up video).
The fault arises when you assume that a family cannot have two daughters named Julie and that a boy cannot have the name Julie. This changes the data provided and makes a seemingly unrelated piece of information (name) vital to the problem. You cannot change between working with purely theoretical numbers based on a perfect world (where both daughters and sons can be named Julie) and working with numbers that are based upon the norm of parental naming choices. If boys can be named Julia and a family can have two daughters named Julie, there would be no paradox.
This is the problem with statistics. It tries to incorporate information that doesn't actually matter.
Not really. These data and their inferences actually DO matter. However, when stats are presented to the general public, the journalist should present the forest and not the trees.
Going a little off topic here:
Instead of mentioning homicides have increased since the 1900s, they should take into consideration the fact that the population has increased and that reportings have increased which might even explain away and real difference in homicides.
Journalists love to hype/exaggerate scientific findings. Coffee is good/coffee is bad. Wine is good/wine is bad. Wine is terrible for your health and coffee is good but I digress.
The nuances do change everything and (correct) math is the truth.
No. Statistics is not the problem. See my solution above.
@@itsover9008 Yes really. The odds of a fair coin having landed on heads is 50/50 every time. Learning other information doesn't change physics, or genetics, or anything else. The likelyhood of an event doesn't change by learning information, ever.
The likelyhood of having two girls is set by genetics. Hearing about the name or hair color or age doesn't change that. Genetics doesn't change because you learned something that you didn't know before. Statistics tries to change genetics by learning what the girl's name is.
Something you learn early in your scholastic career is to weed out information that doesn't impact what you're looking for. Statistics tries to turn that around and make use of useless information.
@@theofanislantzakis9869 You're right. Statistics isn't the problem. People not understanding what information is useful and what isn't is the problem. The name doesn't matter at all.
@@atheistontheroad4545 thats not 100% accurate either.. the name or not name could be important or not.. the problem is in the fact that the probability has no real bearing on the outcome. weather its 33% or 50% doesnt mater since the only outcome that matters is the one that is true. Changing and adding information that changes the percentage is irrelevant to the end result.. you could add information until its 99% that is 2 girls or 1% that its 1 girl but either way either outcome is possible. in reality everything has a 50% possibility.. 1 it is or 2 it is not. but numbers and information can be moved around to determine a likely likelihood.
Actually thought of a great analogy to explain this:
Imagine you're on a beach, searching for yor daughter. You see two people in the distance, and although you can't make out the details, and you're not sure who's closest, you're sure at least one of them is a girl. We then have 3 possibilities, (G,B), (B,G), (G,G), the one on the left being the one closer to you. You get a bit closer, and although you still can't determine who's closest, or the gender of the other person, you're difinitely sure that the other one is your daughter. Now, again with the closest one on the left, we get this distribution: (D,B), (B,D), (D,G) and (G,D). In the first case, only one outcome of the three gave us two girls, but in the second one, it's two out of four. Not sure how helpful this is a year later but i had to share.
(B stands for Boy, D for daughter and G for girl)
Very interesting take :)
Ceasarian sections are rarely performed on weekends, so the odds of being born on a Tuesday are slightly higher than 1/7.
I think you explained some things a bit wrong. Anyway here's how this intuitively makes sense: a parent in a family with 2 children casually mentioning the name of their daughter is is bigger if they have 2 daughters, if they have one of each they could have mentioned the name of their son first in which case you know its not a family with 2 daughters. Even by saying "my daughter's name is..." they have already revealed that they have a daughter before revealing they have a son. Any mention of a daughter increases the chance of having 2 simply bause families with one of each have a 50/50 chance of mentioning their son first.
Welcome to statistical quantum mechanics 101
ooof. haven't seen it completely but its mind-boggling.
@Peter Rabitt that seems more likely. When we know that atleast one is girl, then the order should not matter.
@Peter Rabitt Yeah. I get your point. It was probably planned for 1st April.
@Peter Rabitt the order definitely does matter for this. A family of 2 kids can have either BB, BG, GB, or GG. That isn't an arguing point that's just how this question is set up. So when you know that at least ONE is a girl, you're narrowed down to BG, GB, and GG. Of which, only 1 of the 3 has a girl as the other sibling
@Peter Rabitt if a flip 2 coins and tell you ONE is heads, what is the probability the other is also heads? By your logic it's 50%, which is clearly not right
@Peter Rabitt let's think about real life real families with 2 kids. A family can either have a boy as their first and a boy as their second, a boy as first girl as second, girl as first boy as second, or girl as first girl as second. There is no other way to have girls and boys, that's it. Now since they all have equal probability, the BG and GB as a whole group will be twice as much as just the GG group.
It is not surprising to me. There is extra information in the 'her name is Julie'. The extra information allows us to reasonably assume the other person is not named Julie, and this assumption changes the context thereby changing the calculation
I seek to extrapolate as much information as possible out of everything
The probability does not change reality, only the expectation. Different realities cause people to say different things.
There is a layperson's language problem here. We often talk about "The Probability" as if that is a single concept. But the discussion is about "The Probability of x, *CONDITIONED ON* the following information".
This is comparing Red Apples to Green Apples (not quite Apples to Oranges). They are different situations, and of course can measure differently.
its both 33% and 50- "now its 13/27" doh
@@a.wadderphiltyr1559 eh?
@@a.wadderphiltyr1559 ugh no
What if.... they were twins?
Easily forgettable youtube commenter he says he's assuming for independent events, meaning they can't be twins
Yeah...? And he's asking what if they were.
And with the same name, born on a tuesday
I guess we shouldve assumed the probability of both born on Tuesday is greater than 1/49, but we'd have to know the probability of twins to get the exact number
Hmmmm, does this paradox play a role in the observation of quantum effects?
Wow what a big brain dude 🤯🤤🤤
I'm going out on a limb to disagree about this video.
In my eyes, the dice were rolled WHEN the children were born. Thus, those odds are the ONLY thing that matter to their gender.
Not name, date of birth, or anything. As none of those varibles affect the original dice roll (odds) of it being GG, GB, or BB.
I feel like our brains are logically wired to disagree with this line of thinking, but... The more I think of it this way, the less I agree with the video's math and the commenters' logic.
This reminds me a lot of the Monte Hall Problem. For those of you who don't know, there are 3 doors, let's say A, B, and C. You pick a door, then the host then shows an incorrect door, the asks if you should stay, or switch. Most people think that you then have a 50/50 chance of winning (most people choose to stay partly because of this), but they are wrong. By switching, you have a 66.7% chance of winning, with a 33.3% chance if you stay. This is because in the beginning, you only have a 33.3% chance of getting it right, and because the host will always pick an incorrect door to reveal. The fact that the host always picks an incorrect door, you still only have a 33.3% chance you chose right. If you still don't get it, I'll lay out all the options.
Let's say Door C is the winner in this case.
Pick A -> B is revealed to be incorrect -> Stay -> Lose
Pick B -> A is revealed to be incorrect -> Stay -> Lose
Pick C -> A/B is revealed to be incorrect -> Stay -> Win
Pick A -> B is revealed to be incorrect -> Swap -> Win
Pick B -> A is revealed to be incorrect -> Swap -> Win
Pick C -> A/B is revealed to be incorrect -> Swap -> Lose
As you see, if you stay, there is only 1 out of 3 possibilities you will win, while if you swap, there are 2 out of 3 possibilities you win.
I don't know why, but I like explaining the Monte Hall Problem.
At 10:41, the correct phrase would be "15 percent points", not "15 percent" as you said. Nice topic though! It is counter-intuitive on a superficial level only. Because, the whole idea of probability theory pivots on the idea that the more information you have the more accurately you can calculate the probability. Hence the change of figure. To anyone familiar with Bayesian way of reasoning, this phenomenon would not appear weird at all.
Information not in evidence was assumed, however. Firstly, that all of the pool of b/g//g/b families would indeed refer to their daughter rather than their son. Given no data to support that, the appropriate hypothesis is that half of those families would refer to their son instead of their daughter, and since the man in question referred to his daughter, his family is not one from that pool. Accounting for what information would be shared by de-biasing where information was not given to support the bias gives us 50%s across the board.
Linguistically, when you say "I have two children one of which is a girl..." makes the assertion, unspoken, the other is a boy.
I think you didnt understand it right so you are confusing us. Your calculations were right, no complaining on this.
We have two numbers: 50% and 33%, which you can say both are correct answers, but for different questions.
The probability that you have two daughters is 33% but the probability that julies sibling is a girl is 50%.
So you asking where does the probability rise. Its not like you presented it. When he says I have a daughter named Julie, the probability that he has two girls is still at 33%.
Lets assume you meet one daughter, then there still could be the possibility that this isnt Julie, but when you get the information, that this is Julie, then the probability rises to 50%.
Let me make this very simple to understand.
In the first explaination is the error. You need to count the number of 'girls-with-a-sister' in GG column as *500 instead of 250* because both girls in each element of GG have a SIBLING WHO IS A GIRL..
you can't just count one set of girls to have a girl sister, the other set of girls *also has a sister* by definition. (Reversible relation) (the same way you did in the 'Julie' example.) Which makes all 500 of the elements in GG each have a sister-sibling (as opposed to only 250 girls having a sister-sibling).
So there are 500 'girls-with-a-sister' in 250 families of GG.
And 500 'girls-with-a-sister' in 500 families of BG.
Now's the easy part!
We have
Event (E) = One of the children is a girl.
P(G/E in BG) = 500/1000 = 50%
P(G/E in GG) = 500/1000 = 50%
Hence a 50% chance of having a girl sibling in GG family as well.
Or easier way to say it is, there's a 50% chance of having a girl child *if one of the two is already given to be a girl*
There! Now there's no paradox :)
what helped me understand is that it is identifying which of the two girls a parent is talking about if they have two.