I failed probability last year and retaking it this year. Your explanation of Pr (A|B) using the Venn diagram is so absurdly logical I am floored. It's 100 times easier to see than trying to use numbers and algebra. I've yet to learn how to understand concepts in this 'different' way.
Informal definition + Formal definition + Intuitive explanation of the definition + examples + further insight on future topics=Amazing Video! ...Thanks so much!
someone give this guy a medal. he is clearing my basics, from the past 3-4 years just confused with this topic and has avoided it .have no words for your efforts really thanks a lot for such awesome video
Your explanation of conditional probability using the Venn Diagram just blew my mind. So much easier to grasp the topic when you get an intuitive explanation of the topic.
@@jbstatistics Indeed, i went through a lot of materiaql on YT- and find your elaborations the most natural, relaxed, intuitive and clear. Kudos! ... and BIG Thanks!
I'm having to retake Probability and Statistics this semester after dropping it last and seeing you upload has given me new hope for this semester. Thanks for the great videos man!
this is the best explanation of conditional probability ever. I love how the explanation creates a foundation for what independent events are. thank you sir
This is by far the best explanation I have seen, the visualisation of the notation applied on diagram is really helpful because it tells you the whole story. Thank you (one more subscriber)
Thank you so much for making this video! I just started learning statistic on Coursera, but the teacher there makes it complicated and way too difficult to understand. And then I found your video! You are a life saver. Keep up the good job!
Out of other videos this is superbest and at the top level because of sooo clear explaination i have imediately subscribed it..... Fabulous... Instead of focusing only on solving Qs through formulae .. Explaination of those is also provided.
Your are the best statistics channel out there, thank you! Could you please do a video about equivalence testing? In a world of data sites getting bigger and bigger good old hypothesis tests are not enough anymore
Thank you this video really helped! I've already watched several videos on the topic but they just confused me more :'). Really appreciated the diagram around 4:30 personally.
This is what i had at first: S= (0,1,10,100) A=S1(10,100) B=S2(10) P(B/A) = P(A n B)/ P(A) = (1/4)/ (2/4)=1/2 =0.5 What I did above works if an only if they (payouts) do have the same probabilities.... but the probabilities differ according to the payout. Thanks alot sir
Hi Jb, great videos like other has joyfully pointed out. I’m a bit confused by the wording of example of rolling a dice at 6:19 tho, would you mind clarifying if you had time please? You see the P(A|B) with event A ={1,2,3,4,5,6}, I would interpret it as what is the probability of rolling 1->5 given we have already rolled 3->6. So when the answer is 3/4, which you only took a part that overlap between 2 events, it confuses me a bit.
We are given that event B happens. So the number that comes up on the top face is a 3, 4, 5, or 6. That is our reduced sample space, or, in other words, the little universe in which we now reside. So we're sitting in a universe in which the number is a 3, 4, 5, or 6. What is the probability that A occurs if we are in such a universe? Well, there are 4 equally likely possibilities in this universe, and 3 of them (3, 4, and 5) are in A. So P(A|B) = 3/4. (Since A occurs if the number is a 3, 4, or 5, and doesn't occur if the number is a 6. There are no other possibilities.) When we condition on an event, we are taking as a given that it occurs, so our universe reduces down to the universe in which that event occurs.
@@jbstatistics oh gosh, that makes so much sense, and so speedy!. I’m sorry if this bothers you because you have already explained it in the “Intro vid for conditional probability”. Thank you JB, big help! P/S: Are you coming up with new videos? If you had a course that teaches statistic somewhere, I would totally support it.
@@MinhHaNguyen05 You're very welcome. I'm always happy to help when someone is trying and can't understand something. Conditional probability can be a little tricky, and there aren't many others that explain it in the fashion I do (there are some, to be sure, but most folks on youtube know just enough to jam things into the formula so you don't typically get this take). The conditional probability formula is just a formalization of the logic used in this example. New videos are always part of the plan. Time for new videos is always another story. I'm currently doing a big rewrite of my notes/text and mapping out in my brain what new videos I'd like to make. I'll likely be able to roll new videos out starting in the summer. I don't have an online course anywhere, other than through my university. Thanks for the kind words. I'm happy to be of help.
I was confused by this at first as well. Key realization for me was (being rusty on probability) that the event occurs if any of its numbers are rolled, not if all of them are rolled. Doh
Good explanation.plz if u have ha time can u explain 6:36 that how p(A) = 5/6 and p(A/B) = 3/4 have relation 5/6 is the probability of {1, 2, 3, 4,5} elements out of six {1, 2, 3, 4, 5, 6} but 3/4 is the probability of {3, 4, 5} elements out of { 2, 4, 5, 6} when we reduced it's sample space . Finally I want to ask when we reduced sample space then every element of A is not in reduced sample space
i never swear but u are fucking awesome. I never understood this formula. I watched like 1000 video from making tree to everything. Now i can say i understand this formula. Thanks a lot. If i havent watched this video i wonder how many year i would have struggled
Because "given" means something very different from "and". In the roll of a fair die, the probability of getting a 2 and an even number is 1/6. The probability of getting a 2 *given* it's an even number is 1/3, since we are given the information that the number is a 2, 4, or 6. The probability that a meteorite strikes your house tonight and you die as a result of getting struck by a meteorite is tiny. The probability that you die as a result of a meteorite strike tonight, given a meteorite strikes your house tonight, is pretty high.
@@jbstatistics ok, I understand that they are different, but why divide by P(B)? how youi go from not knowing the formula to knowing it, and knowing that you have to divide it by P(B), why not by P(A)?
@@2radix774 It's from the reduced sample space argument. The sample space has been reduced to B; we know (or are assuming) we are in B. Since B is now our sample space, we need to rescale everything by the probability of B (this will, for example, make the maximum possible conditional probability 1, as it should be). Imagine the probabilities are represented by areas in that Venn diagram. If a dart lands randomly in the sample space, what is the probability it lands in A? B? A n B? P(A), P(B), P(A n B), respectively. Now, if we have the information that the dart landed randomly in region B, what is the probability that dart is also sitting in A? Look at the example I started off with, P(2|Even) when rolling a fair six-sided die. Intuitively, we can see that this conditional probability is 1/3, right? What gets us there, in terms of P(2), P(even), and the probability of their intersection? It’s definitely not P(2 n Even)/P(2), as that turns out to 1 and we know that’s not correct. P(2 n Even)/P(Even) gets us what we know to be the correct value.
you did well, the division part of the conditional probability really threw me off, but the way you explain just made me realize in non-conditional probability, the probability in a sense has a denominator of 1 which signifies "from the whole sample space", when you add given, you must divide to specify its a part of which (partial whole). Thank you. Other videos dont make that clear.
@@jbstatistics O wow, I thought You dont post videos anymore, I was sad to see your last video 1 year ago I thought maybe he left youtube, Now Im happy cause you are still here, probably you're busy with life thats why no new videos
Why does Conditional Probability divide by the given event, but not subtract? When you describe Conditional Probability with the Ven Diagram, my thought about subtracting event B is reinforced. It seems like I would get the same answer by subtracting.
in the red jacks example why aren't we saying that the probability of drawing a jack givin that the card is red would be : (1/13)/(1/2) wouldn't that be the correct representation of the conditional probability law the probability of the intersection 1/13 over the prob of the card being red 1/2 ? can you please explain.
The probability of getting a red jack is 2/52 = 1/26, not 1/13. The intersection of "the card is red" and "the card is a jack" is "the card is a red jack".
There are 2 cards that are both a jack and red (the jack of hearts and jack of diamonds). P(J and R) = 2/52. P(R) = 26/52. P(J and R)/P(R) = (2/52)/(26/52) = 2/26 = 1/13.
Hey I’ve watched a few of your playlists and am just writing this to ask you a general question. What’s the best way to learn statistics stuff in r? I’m an actuarial student I’ve done statistics but I’m just unsure what the best way to learn r. Any advice would be most appreciated
can anyone tell me how this gentlemen has calculated the value of P(A) in the second example, please can anyone tell me? how that value of 0.010 has came up as P(A)? please
I define event A to be the event the person wins more than $1. There are two amounts greater than $1: $10 and $100. Winning $10 and winning $100 are mutually exclusive events, where their individual probabilities are given as 0.009 and 0.001. The probability of winning more than $1, or, in other words, winning $10 or $100, is the sum of those two probabilities.
I go through a detailed explanation of that as best as I am capable of, using a variety of different approaches, including the Venn diagram representation around the 4:00 mark. I can't possibly do any better than that in a text response.
p(b) must be greater than to zero, but when you said that the event in the denominator has already occurred and there is no chance of occurring it then why the P(b) >0 and not equal to zero.
The payout is the amount of money you receive. In the example, you get $1 back with probability 0.301, $10 with probability 0.009, and $100 with probability 0.001. "Payout" has a similar meaning to "winnings" here, but I didn't want to use that word as then there would be some ambiguity as to whether your original $1 purchase price was included in that.
@@jbstatistics I understood sir thank you somuch 😊😊 ,by your explanation I understood sir ,you explanation is great and you explained my doubt too😊😊,I watched many videos but I not understood by them but you explained well sir,I'm new subscriber 😊,once again thank u so much sir🙏🙏🙏😊
Best explanation ever had. I love when he says, please do me a small favour and don't memorise the formula. That's how every teacher should be ❤
I failed probability last year and retaking it this year. Your explanation of Pr (A|B) using the Venn diagram is so absurdly logical I am floored. It's 100 times easier to see than trying to use numbers and algebra. I've yet to learn how to understand concepts in this 'different' way.
Informal definition + Formal definition + Intuitive explanation of the definition + examples + further insight on future topics=Amazing Video! ...Thanks so much!
You're very welcome! It's one of my faves.
Believe me, gentleman, you are really good at this!
Thanks!
someone give this guy a medal. he is clearing my basics, from the past 3-4 years just confused with this topic and has avoided it .have no words for your efforts really thanks a lot for such awesome video
the best explanation I've found about this topic so far, thank you man
people like you who put effort in helping others understand things are just great human beings. thanks
Your explanation of conditional probability using the Venn Diagram just blew my mind. So much easier to grasp the topic when you get an intuitive explanation of the topic.
I watched lots of video on youtube but no one explains as clear then you, now i got conditional probability:) THANKS men
I'm glad to be of help!
Failed my probability test. This is one of the best explanations I've seen on this topic.
I have struggled and struggled with this and came across your video....wow....I FINALLY have it! Thank you so much!
Such high quality content. You have a gift for deepening other human's understanding of this stuff :)
Well, I can't ask for a nicer compliment than that! Thanks so much for the very kind words!
@@jbstatistics Indeed, i went through a lot of materiaql on YT- and find your elaborations the most natural, relaxed, intuitive and clear. Kudos! ... and BIG Thanks!
Thank you for taking the effort to explain the statistical concepts intuitively!
High Quality content, well explained. You sir have my appreciation!
Thanks for the compliment!
this is the best lecture i have ever attended
Thanks so much for the kind words!
I'm having to retake Probability and Statistics this semester after dropping it last and seeing you upload has given me new hope for this semester. Thanks for the great videos man!
You are very welcome! I'm not sure how many I'll be able to produce and upload this semester, but I'll see what I can do!
this is the best explanation of conditional probability ever. I love how the explanation creates a foundation for what independent events are. thank you sir
Thank you so much for the very kind words!
This is by far the best explanation I have seen, the visualisation of the notation applied on diagram is really helpful because it tells you the whole story. Thank you (one more subscriber)
Hallelujah!
Thank you. The first video to actually make me understand instead of assuming that the logic of conditional probability is inherent
This is the first time this has ever made sense to me!! Thank you so much!!!!!
Your explanations are very good. Real life saver
Amazing explanation!!! I like that you explain the formula and don’t just tell us to memorize it
Made perfect sense. Watched several ones before.. but none made it this clear.
Thank you so much for making this video! I just started learning statistic on Coursera, but the teacher there makes it complicated and way too difficult to understand. And then I found your video! You are a life saver. Keep up the good job!
Cristal clear. I love concepts stepping on top of formulae!!!
Thanks!
This is an amazing video, my professor rushed through this in like 2 minutes. Thank you!
Out of other videos this is superbest and at the top level because of sooo clear explaination i have imediately subscribed it..... Fabulous... Instead of focusing only on solving Qs through formulae .. Explaination of those is also provided.
I'm glad you've found this video helpful!
Your are the best statistics channel out there, thank you!
Could you please do a video about equivalence testing? In a world of data sites getting bigger and bigger good old hypothesis tests are not enough anymore
The best video for introductory conditional probability!
The best video on Bayes theorem!
Kudos to you brother!
This video helped me understand the answer to the question I was looking in all the videos .... thank you
Thanks a lot for these great videos. I'm learning a lot more than I did in college lectures.
You are very welcome!
Whatta legend. Helping my masters sail through !
I have a prob and stats quiz tomorrow and this helped me immensely! Thank you very much!
I feel like the probability of me understanding statistics has increased given that I have now watched this video.
Thank you this video really helped! I've already watched several videos on the topic but they just confused me more :'). Really appreciated the diagram around 4:30 personally.
I am enjoying this more than I do with my lecture, thank you Sir
A High level clarity has been provided....with intuitive values.
Most brilliant and super explanation of conditional probability.
Thanks!
Great Job!. The best statistics channel on TH-cam!.
It is indeed :) Thanks Marco!
Thank you so much! I finally understand the conditional probability formula.
Thank you so much for this video! It was really clear and well-explained.
You are very welcome!
I'm 20 years old, i've studied this topic like 4 times and i thought that i had understood it. Now I really understand it
it is the best one i have even see explaining the content thank u !
Good content, good explanation. The calmness of te logic before the formulas.
Fantastic! Especially when you said: do me a favour, don’t try to memorize the formula
This is what i had at first:
S= (0,1,10,100)
A=S1(10,100)
B=S2(10)
P(B/A) = P(A n B)/ P(A) = (1/4)/ (2/4)=1/2 =0.5
What I did above works if an only if they (payouts) do have the same probabilities.... but the probabilities differ according to the payout.
Thanks alot sir
thankyou soo much , before this i was never able to understand conditional probab
Thank you so much for making this video. It is so helpful!!
Everything Just Clicked... You are amazing
i like that you promote logic and intuitive understanding, its the best way to be prepared if you have a deep understanding
Thanks for the kind words. This is definitely not a "how to" channel -- I try very hard to help students develop a deep understanding of the concepts.
Great video, i hope this helps me in the quiz today
That special notice at @4:57 is amazing. Here in the Indian education system unfortunately everything is rote based learning :(
Hi Jb, great videos like other has joyfully pointed out. I’m a bit confused by the wording of example of rolling a dice at 6:19 tho, would you mind clarifying if you had time please?
You see the P(A|B) with event A ={1,2,3,4,5,6}, I would interpret it as what is the probability of rolling 1->5 given we have already rolled 3->6. So when the answer is 3/4, which you only took a part that overlap between 2 events, it confuses me a bit.
We are given that event B happens. So the number that comes up on the top face is a 3, 4, 5, or 6. That is our reduced sample space, or, in other words, the little universe in which we now reside. So we're sitting in a universe in which the number is a 3, 4, 5, or 6. What is the probability that A occurs if we are in such a universe? Well, there are 4 equally likely possibilities in this universe, and 3 of them (3, 4, and 5) are in A. So P(A|B) = 3/4. (Since A occurs if the number is a 3, 4, or 5, and doesn't occur if the number is a 6. There are no other possibilities.) When we condition on an event, we are taking as a given that it occurs, so our universe reduces down to the universe in which that event occurs.
@@jbstatistics oh gosh, that makes so much sense, and so speedy!. I’m sorry if this bothers you because you have already explained it in the “Intro vid for conditional probability”. Thank you JB, big help!
P/S: Are you coming up with new videos? If you had a course that teaches statistic somewhere, I would totally support it.
@@MinhHaNguyen05 You're very welcome. I'm always happy to help when someone is trying and can't understand something. Conditional probability can be a little tricky, and there aren't many others that explain it in the fashion I do (there are some, to be sure, but most folks on youtube know just enough to jam things into the formula so you don't typically get this take). The conditional probability formula is just a formalization of the logic used in this example.
New videos are always part of the plan. Time for new videos is always another story. I'm currently doing a big rewrite of my notes/text and mapping out in my brain what new videos I'd like to make. I'll likely be able to roll new videos out starting in the summer. I don't have an online course anywhere, other than through my university.
Thanks for the kind words. I'm happy to be of help.
@@jbstatistics you are unbelievably kind! Rooting here to learn more from you, JB!
I was confused by this at first as well. Key realization for me was (being rusty on probability) that the event occurs if any of its numbers are rolled, not if all of them are rolled. Doh
Awesome really, the best tutorial about the topic
this is really probably redundant from other videos but you explained what my math teacher tried to do in two weeks
I wish I could touch the like button under this video 1000 times!
This is amazing. Thanks for sharing.
Good explanation.plz if u have ha time can u explain 6:36 that how p(A) = 5/6 and p(A/B) = 3/4 have relation 5/6 is the probability of {1, 2, 3, 4,5} elements out of six {1, 2, 3, 4, 5, 6} but 3/4 is the probability of {3, 4, 5} elements out of { 2, 4, 5, 6} when we reduced it's sample space .
Finally I want to ask when we reduced sample space then every element of A is not in reduced sample space
i never swear but u are fucking awesome. I never understood this formula. I watched like 1000 video from making tree to everything. Now i can say i understand this formula. Thanks a lot. If i havent watched this video i wonder how many year i would have struggled
Sir, believe me, you are God of statistics.
Thanks!
4:54 BUT why isn't the probability P(A|B) just equal to P(A intersection B)? why do you need to divide it by P(B)?
Because "given" means something very different from "and". In the roll of a fair die, the probability of getting a 2 and an even number is 1/6. The probability of getting a 2 *given* it's an even number is 1/3, since we are given the information that the number is a 2, 4, or 6. The probability that a meteorite strikes your house tonight and you die as a result of getting struck by a meteorite is tiny. The probability that you die as a result of a meteorite strike tonight, given a meteorite strikes your house tonight, is pretty high.
@@jbstatistics ok, I understand that they are different, but why divide by P(B)? how youi go from not knowing the formula to knowing it, and knowing that you have to divide it by P(B), why not by P(A)?
@@2radix774 It's from the reduced sample space argument. The sample space has been reduced to B; we know (or are assuming) we are in B. Since B is now our sample space, we need to rescale everything by the probability of B (this will, for example, make the maximum possible conditional probability 1, as it should be).
Imagine the probabilities are represented by areas in that Venn diagram. If a dart lands randomly in the sample space, what is the probability it lands in A? B? A n B? P(A), P(B), P(A n B), respectively. Now, if we have the information that the dart landed randomly in region B, what is the probability that dart is also sitting in A?
Look at the example I started off with, P(2|Even) when rolling a fair six-sided die. Intuitively, we can see that this conditional probability is 1/3, right? What gets us there, in terms of P(2), P(even), and the probability of their intersection? It’s definitely not P(2 n Even)/P(2), as that turns out to 1 and we know that’s not correct. P(2 n Even)/P(Even) gets us what we know to be the correct value.
Thank God for your channel !
Great work sir. Keep going👍
Absolutely clear explanation
Thanks!
jbstatistics is there any video on multiplication theorem of probability
you did well, the division part of the conditional probability really threw me off, but the way you explain just made me realize in non-conditional probability, the probability in a sense has a denominator of 1 which signifies "from the whole sample space", when you add given, you must divide to specify its a part of which (partial whole). Thank you. Other videos dont make that clear.
So hight quality cours. Thanks alot!
your videos are really good. great job!
If i was able, I would definitely give this person a, "NOBEL PRIZE" 🏆🏆🏆
Thanks! I'd accept it!
Very helpful statistics videos
finally found the right Channel,
I've been waiting!
@@jbstatistics O wow, I thought You dont post videos anymore, I was sad to see your last video 1 year ago I thought maybe he left youtube, Now Im happy cause you are still here, probably you're busy with life thats why no new videos
Excellent. Very helpful video
Why does Conditional Probability divide by the given event, but not subtract?
When you describe Conditional Probability with the Ven Diagram, my thought about subtracting event B is reinforced. It seems like I would get the same answer by subtracting.
in the red jacks example why aren't we saying that the probability of drawing a jack givin that the card is red would be : (1/13)/(1/2) wouldn't that be the correct representation of the conditional probability law the probability of the intersection 1/13 over the prob of the card being red 1/2 ? can you please explain.
The probability of getting a red jack is 2/52 = 1/26, not 1/13. The intersection of "the card is red" and "the card is a jack" is "the card is a red jack".
This video is amazing!
nice, very precise n clear. helpful video
how to calc. the jack example by using the formula? i have P(J and R)/P(R), which yields 2/13. why is it wrong? thanks
There are 2 cards that are both a jack and red (the jack of hearts and jack of diamonds). P(J and R) = 2/52. P(R) = 26/52. P(J and R)/P(R) = (2/52)/(26/52) = 2/26 = 1/13.
Awesome explanation... Thank you
Can anyone explain me why he took p(A)=0.010 instead 0.009 at 9.23???
Great videos. I wish I found your page earlier in the semester.
It's a really helpful thank you very much for this video 👍👌
You are very welcome!
Hey I’ve watched a few of your playlists and am just writing this to ask you a general question. What’s the best way to learn statistics stuff in r? I’m an actuarial student I’ve done statistics but I’m just unsure what the best way to learn r. Any advice would be most appreciated
REALLY NICE VIDEO. THANK YOU SO MUCH!!!!
can anyone tell me how this gentlemen has calculated the value of P(A) in the second example, please can anyone tell me? how that value of 0.010 has came up as P(A)?
please
I define event A to be the event the person wins more than $1. There are two amounts greater than $1: $10 and $100. Winning $10 and winning $100 are mutually exclusive events, where their individual probabilities are given as 0.009 and 0.001. The probability of winning more than $1, or, in other words, winning $10 or $100, is the sum of those two probabilities.
@@jbstatistics get it thank you 👍🏽😎
wouldn't the payout is more than $1 be event B as it is the 'given that' condition?
A and B are just arbitrary labels on the events; it doesn't matter which event is called A and which is called B.
Awesome video! Thanks
thank you so much,,your videos are very helpful
,,,,it would be nice if you create a playlist Probability theory for Machine Learning
Hi there, is there a video on conditional random variable? I'm very lost on that particular topic when trying to understand the subject
I don't have a video on conditional random variables yet. There are likely some on TH-cam, but I haven't looked and I don't know of any.
@@jbstatistics I did try watching the other videos, but theirs were not as sweet, short and concise as yours was :(
@@weiqiaocheng9185 I believe you :)
@@jbstatistics is it possible to ask you questions? Maybe through an email or something? 😅
@@weiqiaocheng9185 No. I sometimes answer questions here if they're directly related to the videos, but I don't have time to offer general help.
great things sir. which software are you using for this video
In the formula why we have to divide p(b).... please answer to this question
I go through a detailed explanation of that as best as I am capable of, using a variety of different approaches, including the Venn diagram representation around the 4:00 mark. I can't possibly do any better than that in a text response.
Please... Please... Do Bayes theorem . It's a critical follow up on conditional probability.
How can I give you many for all of this?
thank you . can you make tutorial on other subject of math like calculus / geometry ?
p(b) must be greater than to zero, but when you said that the event in the denominator has already occurred and there is no chance of occurring it then why the P(b) >0 and not equal to zero.
Very nice vdeos in probability
Thanks for your video, this is awesome
Thank you for share the videos ..!!
thank you so much!!! this is super helpful!!
ty!! i understand where the formula comes from now!
Sir you explained well,but what is mean that payout?
The payout is the amount of money you receive. In the example, you get $1 back with probability 0.301, $10 with probability 0.009, and $100 with probability 0.001. "Payout" has a similar meaning to "winnings" here, but I didn't want to use that word as then there would be some ambiguity as to whether your original $1 purchase price was included in that.
@@jbstatistics I understood sir thank you somuch 😊😊 ,by your explanation I understood sir ,you explanation is great and you explained my doubt too😊😊,I watched many videos but I not understood by them but you explained well sir,I'm new subscriber 😊,once again thank u so much sir🙏🙏🙏😊
@@saichaitanyamaths8234 You are very welcome!
@@jbstatistics ❤❤❤