Sal, you are a Hero. The world will remember you for centuries, for the work you've done. You will help milions of students with thse videos :D But you already know that :D I wanted just to say Ty, and Good job :D
I don't understand why professors often don't give a concrete example of where these theorems and laws could apply. Without them, there's a big chance that a lot of people won't know what they are dealing with, so I thank you a thousand times for this video !
To put simply - Even if you carried out a routine 100 times where you flip a coin a fixed amount of times and found that it always landed on heads 70% if the time, you cant use that as concrete evidence to decide there is a 70% chance the coin will always land on heads. For example, it may land on heads 40% of the time if you repeated the routine another 100 times.
The reason the law of large numbers works is because the odds are not changed by the past. If you flip a fair coin 100 times and get 64 heads, you have 64% heads. If you flip the coin 900 times more, you are most likely to get 450 more, for a total of 514 of 1000, that is now 51.4% heads. Those 64 heads have become a smaller percent of the 1000 tosses. Flip 10,000 times and those 64 heads are are now even less of the percent.
So my friend and I had a huge talk about this concept being applied to Avengers Infinity War. Basically half of all life gets snapped out of existence. He says because the law of large numbers, the number of humans on Earth would be about half because 7 billion is a very large number and there was no partitioning among races or planets. I said that 7 billion is an extremely small number relative to living life in a universe filled with aliens and bacteria so the law of large numbers does not come into effect so there should be an arbitrary number of humans alive. An analogy I used is taking a scoop of sand from the Sahara desert (which is looking at the human race) and making a claim that because there is a lot of grains of sand (humans) that it represents the whole desert’s elemental make up (the other google life forms). Who is right?
I agree with your friend. Try to look this another way, every person has a 0.5 probability of dying and there are 7B people which is pretty large so the number of people dying would tend to be 3.5B.
Over an infinite # of trials, the mean will converge to the expected value. Key being "an infinite # of trails". Khan also mentions how casino's control the parameters of the game.
One way of thinking about it is that, say you've made n trials, and in ALL of them you got ALL (100) heads, the law o large numbers states that you can pretty much throw completely away all of your past trials, since you're have infinite trials yet to come, and from there your average will tend to 50% as you approach infinite trials. In this way you don't have the wrong intuition that the law would "make up" for your past trials. Instead, they are more like thrown away.
Um.. you basically explained this with circular reasoning. At the beginning of the video: "I'll tell you why this works..", and later "it will converge.... because the LLN says it will converge?" :/
A fair coin is tossed a large number of times. Does the Law of Large Numbers assure us that, if n is large enough, with probability ≥ 0.99 the number of heads that turn up will not deviate from n/2 by more than 100?
Laws of large number does not prevent the massive fluctuation of standard deviation in a given event, it just ensures that massive fluctuations in standard deviation will be balanced out by a standard deviation fluctuation in the opposite magnitude, as the number of events keep increasing.
> if we increase N from 3 to 30; well having a percentage of 66.666 for heads and a 33.333% for tails is not as probable as before If it is not probable as before this means that the more you get heads only your probability of having next a tail next increases. Am I right ? In other words it makes sense to gamble on tails when you have too much heads, even if you cannot be sure ever....
You could say, for example, let's assume we have a table of 100 cells. Flip a fair coin 100 times. List the outcome, heads (H) or tails (T), in the cell commencing with the first cell and continuing consecutively to the 100th cell. How many different tables could be formed? ANS: 2^100 or 1,267,650,600,228,229,401,496,703,205,376 different tables. If each cell was a 1/4" square (1/4" x 1/4") the area so produced would cover the planet earth slightly over 10 tera-times. But don't let that smother any certainty that if "You're not in it you definitely can't win it!" Applied to unweighted outcomes like a lottery the Law of Large Numbers would expect a loser, as that outcome is the most likely. A theoretical mathematical fact that only the self-delusional ignore. On the other hand gambling casinos where the outcome is weighted to assure players win and then with that crisp thrill that only random shock can provide benefit the house. Because then players will continue to play yet in the long run the house, favored by the weighting, gets the greater share of the wins.
here at 6:46 khanacademy says there is a "low probability of this happening", referring to your average being at 70. But if there is a low probability of this happening it means that there is a higher probability that when the average rise you get contrary results in your tosses ... Where am I wrong ?
Even khanacademy at a certain point in the vid chart a line very above 50 and says this is not very probable. But if this is not very probable when you see such a result in your tosses you can rationally start betting the other way around, and somewhat confirms the "gambler's fallacy". Not sure if I get it right, I'm here to learn
7:30 But as an event repeats itself through time, the probability that it doesn't on the next trial does increase, doesn't it? After all, let P1 be the probability of a certain event happening. Then the probability that it happens n consecutive times is P1^n and the probability that it doesn't is 1-P1^n. If P1 is great than 0 and less than 1, the limit of this expression as n approaches infinity is 1-0=1. Such event could be for example the average being above 50... right?
barney boy In Australia, Saturday night lotto went from 40 ball in 1972 then from 1985 the numbers were increased to 45 balls. Too many winners as the number of entries increased. In this case there is to me a force in the tumbler that decides what numbers will be drawn it is mind blowing (to me) Let me explain when the 40 balls were drawn they worked to the law of large numbers, this we would expect. With the remaining 5 balls that were added 13 years later you would expect a lower count of them coming up if we plot them over 46 years. This is how they fall in September 2018, from 1972 till today the lowest number drawn is 17 (seventeen) 285 times and the highest number drawn is 11 (eleven) 345 times. For the 5 balls 41 to 45 that were added in 1985 the lowest drawn number is 44 , at 283 and the highest is 42 at 319 times. The 5 balls that were added later are at times exceeding the original 40 balls. To a person who did not know that 5 balls were inserted 672 draws later would say this shows the laws of higher numbers is correct. The above information says this is not true. Try explaining that.
I heard of this theory in reference to the documentary and movie on the MIT blackjack team. So I wanted to see exactly what it was about. But then you mention gamblers falacy and it sounds like you doubt they had a system for winning long term. Or am I taking your comment out of context.
This Law of Large Numbers works so well for casinos that THEY are the ones getting the biggest jackpots from the poor suckers who empty their wallets! This is scary for sure!
Is it fair to say that not knowing what the expected mean is, what the law of large numbers really tells us is that du/dn = 0 (with u the sample mean and n the number of trials) when the n tends to infinity? or in another words that the sample mean remains constant and that is what we call the expected mean
Haha I completely agree with you!! I was so wrongly misguided about this video title. All I see are some n's and x's going everywhere. NO LARGE NUMBERS!!! So very disappointed...
@Cityj0hn i disagree STRONGLY whit that statement as food water and an oxygen mix is what is the most worth, further more education is not important at all, knowledge how ever is.( yes there is a difference)
Great video. You really explain how as a sample gets bigger, we get a better estimate of our population. Thorough. I have an AP Statistics final tomorrow. Thank you.
1) if i flip the coin 100 times and i get all head, it doesnt mean that i get a tail in 101 flip because every flip is independent. 2) the law of large number said if i go infinity flip, i will converge to the probability of 50% head. that mean tail will have more probability in the rest of the flip. but if i go infinity enough and still get head in every flip, that mean i can sure enough to get tail in the next flip, but they are still independent? 3) isnt the probability of getting 50 head of 100 flip is 100C50 divide by 2^100 which is not 50%? even i approach infinity let say 1000C500 divide by 2^1000. it didnt seem to approach 50%. I just cant link all the concept together? can anyone help me pls.
+Loh Simon If you go to infinity, you must get the expected value, but there's no 'must' before then, because the flips are still independent. The flips are independent when n = infinity, but when n = infinity you are also sure that the sample mean = the population mean.
@Partyffs Knowledge and wisdom can be acquired simply by thinking, however if the thinker has a low IQ nothing will come of it. M.Kaku built a particle accelerator when he was 15 from junk yard parts. Education manipulates the brains to grow, do not be mistaken to think education is the thing you get in schools or colleges. Should I ever fall on the head and lose my intelligence after knowing its value, I would probably want to stop using oxygen and food as well.
Its been a long time since I was searching good lectures on Time series. None of those lectures are inclusive or clearly explained. Then, suddenly khan academy came to my mind . Then I search khan academy for the time series . Extremely happy to see that khan academy have it. I got relief. Lifesaving lectures. Thanks a lot.
Am i the only one here?...dude u were saying that since u had a lot of heads that doesnt mean that there are going to be tails...though u were drawing the average to fall..which means that u got more tails..
Not really. What it means is that at "N"th trial, say your average is 70, but still if you keep trying for infinite amount of times, the average will converge to 50. Now this in fact can happen, though not necessarily, by getting just more heads than tail (but getting less number of heads than average value). But again, this also dose not happen necessarily, but it's one of the rare cases that contradicts your point. Hope you understood.
It's saying that the average will fall but it has infinity tries to get there, not over a fixed number like 1000 or a million tries. The Gambler's fallacy is that things will average out in their favor when in fact, they don't have infinite money to try and the odds are also usually not 50/50.
so if flipping this coin a numerous amount of times after he is up at 70 doesn't guarantee that he gets tails more in the future, then why is there a guarantee that the average drops back down to 50% eventually??????
If there is a series of flips that results in heads that reaches 70, there will be an equal likelyhood of a series of tail flips that reaches 70 as well in a infinite series of coin flips. Not saying it is a guarantee but it means not coming to a conclusion when you see a series of head flips but to consider the rest of the results in the infinite sample. Well, that is how i understand it. haha
It's kinda nice to think about it. Suppose we toss 100 coins and 70 of them are tails. If we continue to toss 2 billions more time with equal probability then we might have something around 1000000070 tails and 1000000000 and they are pretty much 50%
If you flip a fair coin 10 times and it's all head, what is the probability that the result is a head in the 11th times? It's still 50%. Each time you flip a coin, the probability is always 50%. If you think the probability of having a head is less than 50% (which a lot of people do), you have fallen into the gamblers fallacy.
At 6:45, you said that the deviation from the expected value (more heads) is a low probability. What makes that so? Wouldn't this support the gambler's fallacy? Can a probability be calculated how many heads will occur (or not) after a series of consecutive flips that result in heads?
It's a low probability to get heads 10 times in a row. 1/1024. However, this only apply's to one trial of 10 coin flips. In the real world, there are countless trials occurring every day so when you see a rare event like this happening in a casino for example (say 10 red in a row in roulette) it is nothing special since there have been millions of spins previously and the probability of eventually getting 10 reds in a row approaches 1 as the number of trials approach infinity. Mathematically it works like this, probability of 10 heads in a row is 1/1024. So the probability of not getting 10 heads in a row is 1023/1024. The probability of not getting 10 heads in a row after n trials in (1023/1024)^n. As you can see, this will approach zero.
> But if you ask "What is the probability that AFTER I've got 10 heads to get another head at the next toss?", well, this probability will be a small one. Thanks for you reply. This is the part I don't get. If after 10 heads the probability of having a head again is small, than it isn't 50 %, as it should be..... In other words, if a certain series has a 0.0004 probability (10 successive heads), then each time we get a new head the probability of a new successive head should diminish....
That doesn't make sense. You would require more tails to bring the average back down towards 50%. I understand the odds remain the same, but the probability should increase to see more tails after see more heads.
This is one of the highest quality 240p videos I have ever seen
speaking facts
In all videos of 240p there’s gonna be someone with the highest quality and this is
Bc you dont see much pixels. You see colors. Black and lines with colors
how large is your observation set :P
Sal, you are a Hero. The world will remember you for centuries, for the work you've done. You will help milions of students with thse videos :D But you already know that :D I wanted just to say Ty, and Good job :D
:D
agree
My father always says: "Chance has no memory" to describe the gambler's fallacy.
this should be written on casinos walls
I don't understand why professors often don't give a concrete example of where these theorems and laws could apply. Without them, there's a big chance that a lot of people won't know what they are dealing with, so I thank you a thousand times for this video !
gambler's fallacy is the most important thing I learn from this video. Thanks!
Bernoulli surely loved to shake his shoe boxes.
what does this guy doesn't know?
To put simply - Even if you carried out a routine 100 times where you flip a coin a fixed amount of times and found that it always landed on heads 70% if the time, you cant use that as concrete evidence to decide there is a 70% chance the coin will always land on heads. For example, it may land on heads 40% of the time if you repeated the routine another 100 times.
Oh God, my donation to you can the fixing your audio for free. Please contact me if you're interested but holy crap that was painful
bruh
But WHY does this law tend to average out over time? If events were truly independent I don't understand why it would behave this way.
Because we live in a simulation LUUUUUL
The reason the law of large numbers works is because the odds are not changed by the past. If you flip a fair coin 100 times and get 64 heads, you have 64% heads. If you flip the coin 900 times more, you are most likely to get 450 more, for a total of 514 of 1000, that is now 51.4% heads. Those 64 heads have become a smaller percent of the 1000 tosses. Flip 10,000 times and those 64 heads are are now even less of the percent.
🤯
MY BRAINS GONNA EXPLODE!!!
You still alive?
So my friend and I had a huge talk about this concept being applied to Avengers Infinity War.
Basically half of all life gets snapped out of existence. He says because the law of large numbers, the number of humans on Earth would be about half because 7 billion is a very large number and there was no partitioning among races or planets.
I said that 7 billion is an extremely small number relative to living life in a universe filled with aliens and bacteria so the law of large numbers does not come into effect so there should be an arbitrary number of humans alive. An analogy I used is taking a scoop of sand from the Sahara desert (which is looking at the human race) and making a claim that because there is a lot of grains of sand (humans) that it represents the whole desert’s elemental make up (the other google life forms).
Who is right?
I agree with your friend. Try to look this another way, every person has a 0.5 probability of dying and there are 7B people which is pretty large so the number of people dying would tend to be 3.5B.
Watch it in 1.25X or 1.5X and save your time :,-)
me with almost all videos
idk what i studied just now... it's not in my syllabus but i understood everything n im interested,, thanks!!
Sir. I wont economices theory's and large inframtion send me plz
Over an infinite # of trials, the mean will converge to the expected value. Key being "an infinite # of trails". Khan also mentions how casino's control the parameters of the game.
Exactly what i need for studying for my Math class!!!!
sorry guys but this video is for educated people not for people who want to see large numbers.
So the larger the number the more you can closely predict the outcome.
Infinite is a good word ! Haha, explains everything.
One way of thinking about it is that, say you've made n trials, and in ALL of them you got ALL (100) heads, the law o large numbers states that you can pretty much throw completely away all of your past trials, since you're have infinite trials yet to come, and from there your average will tend to 50% as you approach infinite trials.
In this way you don't have the wrong intuition that the law would "make up" for your past trials. Instead, they are more like thrown away.
Um.. you basically explained this with circular reasoning. At the beginning of the video: "I'll tell you why this works..", and later "it will converge.... because the LLN says it will converge?" :/
this is one of the most round about number orientated video I have ever seen on this topic.
A fair coin is tossed a large number of times. Does the Law of Large Numbers assure us that, if n is large enough, with probability ≥ 0.99 the number of heads that turn up will not deviate from n/2 by more than 100?
2020, Thanks Sir!
Laws of large number does not prevent the massive fluctuation of standard deviation in a given event, it just ensures that massive fluctuations in standard deviation will be balanced out by a standard deviation fluctuation in the opposite magnitude, as the number of events keep increasing.
This is what life is.
We have an infinite number of trials left :P
Death : sure, you have
So poisson distribution?
> if we increase N from 3 to 30; well having a percentage of 66.666 for heads and a 33.333% for tails is not as probable as before
If it is not probable as before this means that the more you get heads only your probability of having next a tail next increases. Am I right ? In other words it makes sense to gamble on tails when you have too much heads, even if you cannot be sure ever....
You could say, for example, let's assume we have a table of 100 cells. Flip a fair coin 100 times. List the outcome, heads (H) or tails (T), in the cell commencing with the first cell and continuing consecutively to the 100th cell. How many different tables could be formed? ANS: 2^100 or 1,267,650,600,228,229,401,496,703,205,376 different tables. If each cell was a 1/4" square (1/4" x 1/4") the area so produced would cover the planet earth slightly over 10 tera-times.
But don't let that smother any certainty that if "You're not in it you definitely can't win it!"
Applied to unweighted outcomes like a lottery the Law of Large Numbers would expect a loser, as that outcome is the most likely. A theoretical mathematical fact that only the self-delusional ignore.
On the other hand gambling casinos where the outcome is weighted to assure players win and then with that crisp thrill that only random shock can provide benefit the house. Because then players will continue to play yet in the long run the house, favored by the weighting, gets the greater share of the wins.
here at 6:46 khanacademy says there is a "low probability of this happening", referring to your average being at 70. But if there is a low probability of this happening it means that there is a higher probability that when the average rise you get contrary results in your tosses ... Where am I wrong ?
Even khanacademy at a certain point in the vid chart a line very above 50 and says this is not very probable. But if this is not very probable when you see such a result in your tosses you can rationally start betting the other way around, and somewhat confirms the "gambler's fallacy". Not sure if I get it right, I'm here to learn
7:30 But as an event repeats itself through time, the probability that it doesn't on the next trial does increase, doesn't it? After all, let P1 be the probability of a certain event happening. Then the probability that it happens n consecutive times is P1^n and the probability that it doesn't is 1-P1^n. If P1 is great than 0 and less than 1, the limit of this expression as n approaches infinity is 1-0=1. Such event could be for example the average being above 50... right?
Your looking at each trial individually. The probability doesn't change.
This probability playlist was so great!. Sal, could you add some videos about the inclusion-exclusion method?
barney boy
In Australia, Saturday night lotto went from 40 ball in 1972 then from 1985 the numbers were increased to 45 balls. Too many winners as the number of entries increased. In this case there is to me a force in the tumbler that decides what numbers will be drawn it is mind blowing (to me) Let me explain when the 40 balls were drawn they worked to the law of large numbers, this we would expect. With the remaining 5 balls that were added 13 years later you would expect a lower count of them coming up if we plot them over 46 years. This is how they fall in September 2018, from 1972 till today the lowest number drawn is 17 (seventeen) 285 times and the highest number drawn is 11 (eleven) 345 times. For the 5 balls 41 to 45 that were added in 1985 the lowest drawn number is 44 , at 283 and the highest is 42 at 319 times. The 5 balls that were added later are at times exceeding the original 40 balls. To a person who did not know that 5 balls were inserted 672 draws later would say this shows the laws of higher numbers is correct. The above information says this is not true. Try explaining that.
I heard of this theory in reference to the documentary and movie on the MIT blackjack team. So I wanted to see exactly what it was about. But then you mention gamblers falacy and it sounds like you doubt they had a system for winning long term. Or am I taking your comment out of context.
If I'm ever able to adequately repay you for how much you've helped me Sal, I will make sure I do it.
I am confused. Using same theory can't I say that it will not be equal to population mean ?
This Law of Large Numbers works so well for casinos that THEY are the ones getting the biggest jackpots from the poor suckers who empty their wallets! This is scary for sure!
Is it fair to say that not knowing what the expected mean is, what the law of large numbers really tells us is that du/dn = 0 (with u the sample mean and n the number of trials) when the n tends to infinity? or in another words that the sample mean remains constant and that is what we call the expected mean
very confusing still
It is still useful after 15 years
I haven't even taken a stats class and I still love watching!
nerd
@@cloroxbleach5593 bleach
Thinking pinoy brought me here😂😂😂
same hahahaahaha
Haha I completely agree with you!! I was so wrongly misguided about this video title. All I see are some n's and x's going everywhere. NO LARGE NUMBERS!!! So very disappointed...
@Cityj0hn i disagree STRONGLY whit that statement as food water and an oxygen mix is what is the most worth, further more education is not important at all, knowledge how ever is.( yes there is a difference)
Great video. You really explain how as a sample gets bigger, we get a better estimate of our population. Thorough. I have an AP Statistics final tomorrow. Thank you.
1) if i flip the coin 100 times and i get all head, it doesnt mean that i get a tail in 101 flip because every flip is independent.
2) the law of large number said if i go infinity flip, i will converge to the probability of 50% head. that mean tail will have more probability in the rest of the flip. but if i go infinity enough and still get head in every flip, that mean i can sure enough to get tail in the next flip, but they are still independent?
3) isnt the probability of getting 50 head of 100 flip is 100C50 divide by 2^100 which is not 50%? even i approach infinity let say 1000C500 divide by 2^1000. it didnt seem to approach 50%.
I just cant link all the concept together? can anyone help me pls.
+Loh Simon If you go to infinity, you must get the expected value, but there's no 'must' before then, because the flips are still independent.
The flips are independent when n = infinity, but when n = infinity you are also sure that the sample mean = the population mean.
intuative? I have no idea what you're talking about :)
Back to school for me ;)
@Partyffs
Knowledge and wisdom can be acquired simply by thinking, however if the thinker has a low IQ nothing will come of it. M.Kaku built a particle accelerator when he was 15 from junk yard parts. Education manipulates the brains to grow, do not be mistaken to think education is the thing you get in schools or colleges.
Should I ever fall on the head and lose my intelligence after knowing its value, I would probably want to stop using oxygen and food as well.
After a lot of attempts , I could understand this❤
Even though I'm far past the subject I just Love some of these video's.
Education is worth so much more than anything else.
I love this guy
Thank-you. You explained very clear. got this concept man!
Thumbs up if anyone here is thinking of an online game while learning gambler's fallacy.
How has his voice not changed in 11 years.
Thank You Khan Academy. My statistics professor is terrible.
Me too. That's why I came back to learn statistics again years later since my graduation
@btnheazy03 they dig lil holes and put lil girls in it and then put earth on top.
Thank you so much for this statistics vids!!! I really hope there'll be more soon.
Thank youuu! I missed school when they took notes for this!
hey sal you should make videos about graphs. bar, pi it's really lacking on the site
But why does he times 100 by 5 and get 50.He said Number trials to be times the probability of success of any trials .So is it 50 or 500 .
is not 5 thats a .5 :/ in other words his multiplying by half
Thank you,it makes sense now .
Its been a long time since I was searching good lectures on Time series. None of those lectures are inclusive or clearly explained. Then, suddenly khan academy came to my mind . Then I search khan academy for the time series . Extremely happy to see that khan academy have it. I got relief. Lifesaving lectures. Thanks a lot.
Hmm...maybe i should start whit something more easy to follow,
Anti mater time :D
I can only say is that I wish I had your brain. lol
😊😊😊 1:50
are sample mean and expected value you talked about not same???
they are same
Could this be used in sales results?
So this is why neural networks work
Thank you you've really helped me
As you can see from this formula.... YOU DON'T EVEN LIFT.
Am i the only one here?...dude u were saying that since u had a lot of heads that doesnt mean that there are going to be tails...though u were drawing the average to fall..which means that u got more tails..
Not really. What it means is that at "N"th trial, say your average is 70, but still if you keep trying for infinite amount of times, the average will converge to 50. Now this in fact can happen, though not necessarily, by getting just more heads than tail (but getting less number of heads than average value). But again, this also dose not happen necessarily, but it's one of the rare cases that contradicts your point. Hope you understood.
It's saying that the average will fall but it has infinity tries to get there, not over a fixed number like 1000 or a million tries. The Gambler's fallacy is that things will average out in their favor when in fact, they don't have infinite money to try and the odds are also usually not 50/50.
can you do some card probability video?
The house always wins.
so how do you explain china's skewed male/female population?
An outlier
It all makes sense now
Great video sir. Very easy to understand.
Gambling is cool.
Great
Well explained
so if flipping this coin a numerous amount of times after he is up at 70 doesn't guarantee that he gets tails more in the future, then why is there a guarantee that the average drops back down to 50% eventually??????
If there is a series of flips that results in heads that reaches 70, there will be an equal likelyhood of a series of tail flips that reaches 70 as well in a infinite series of coin flips. Not saying it is a guarantee but it means not coming to a conclusion when you see a series of head flips but to consider the rest of the results in the infinite sample.
Well, that is how i understand it. haha
It's kinda nice to think about it. Suppose we toss 100 coins and 70 of them are tails. If we continue to toss 2 billions more time with equal probability then we might have something around 1000000070 tails and 1000000000 and they are pretty much 50%
If you flip a fair coin 10 times and it's all head, what is the probability that the result is a head in the 11th times? It's still 50%. Each time you flip a coin, the probability is always 50%. If you think the probability of having a head is less than 50% (which a lot of people do), you have fallen into the gamblers fallacy.
infinity is a large number
Because there is no guarantee that he stays up.
At 6:45, you said that the deviation from the expected value (more heads) is a low probability. What makes that so? Wouldn't this support the gambler's fallacy? Can a probability be calculated how many heads will occur (or not) after a series of consecutive flips that result in heads?
It's a low probability to get heads 10 times in a row. 1/1024. However, this only apply's to one trial of 10 coin flips. In the real world, there are countless trials occurring every day so when you see a rare event like this happening in a casino for example (say 10 red in a row in roulette) it is nothing special since there have been millions of spins previously and the probability of eventually getting 10 reds in a row approaches 1 as the number of trials approach infinity. Mathematically it works like this, probability of 10 heads in a row is 1/1024. So the probability of not getting 10 heads in a row is 1023/1024. The probability of not getting 10 heads in a row after n trials in (1023/1024)^n. As you can see, this will approach zero.
2020: 5332
You are awesome Khan
Thank you so much for the lecture videos ! it was very helpful to understand probability :)
best explanation ever
So does this disprove the theory of evolution
No. Evolution is a fact supported by literal tons of evidence
Thank you verry much! Way to go!
> But if you ask "What is the probability that AFTER I've got 10 heads to get another head at the next toss?", well, this probability will be a small one.
Thanks for you reply. This is the part I don't get. If after 10 heads the probability of having a head again is small, than it isn't 50 %, as it should be.....
In other words, if a certain series has a 0.0004 probability (10 successive heads), then each time we get a new head the probability of a new successive head should diminish....
Each flip is independent of the previous flips. The coin doesn't remember what it had the last 10 flips. It's still 50/50
Great!
is this seriosuly something someone needs to learn? it's like telling someone what gravity does
so, the probability of getting a head or a tail will be equal to 50% only at infinity i.e. never??? Is it?
not very intuitive, not very precise, not good enouth
That doesn't make sense. You would require more tails to bring the average back down towards 50%. I understand the odds remain the same, but the probability should increase to see more tails after see more heads.
for infinity it would be 50%
I luv u. i want to have your babies.