that moment wen hours of study are cleared by a 12 minute video no wonder the MIT is number one wish i had 200k to spend in that college unfortunatelly poor scores and have no money... the bright side is that i can calculate the probs of getting there anyway thanks MIT
Amazing video. I have watched so many long videos about conditional probability. This video is very dense, clear, and right on the point. I am going to watch the rest of the videos through this channel
Great vid! Just a caveat for the viewers about the medical tests. He forgot to mention he was specifically talking about screening tests for rare but horrible diseases in the general population. Normally when your doctor orders a test, your prior probability is a lot higher than the prevalence in the general population. Let's say because you have symptoms fitting the disease, your prior is 1 in 10 instead of 1 in 1000. Now the test is suddenly very useful. By testing positive, you go from 10% to 92% probability of having the disease.
Thank you! I have watched many other videos and could not grasp the essence of differentiating P(A|B) from P(B|A). Your example was practical and clear. :)
Amazing explanation! Thank you very much ... if we consider this problem with the same setting, the accuracy of the test need to be around .99999% instead of .99% to achieve .99% of accuracy in the real world! Now I have a more clear understanding why is so difficult to introduce a machine (i.e a deep learning system that analyses histology slides) that makes a clinical diagnosis in the real world.
Amazing one. Now, I can understand basic topics of Information Theory and Coding and Communication Systems lectures well. No more Bayes'' rule and facepalm. :D
I have a doubt.Why do we multiply the probabilities of Blue marble and Blue marble in the tree diagram while we perform a summation - p(b1&y2)+p(y1&y2) to arrive at p(y2)?
I have a doubt. I am confused as to why are we able to multiple the probabilities in the cases of P(B1 and B2), P(B1 and Y1) etc. If we are NOT doing replacement, the events are dependent on each other. And the multiplication rule applied to independent events only right? Can someone help?
06:40 Why do we _multiply_ them? What's the reasoning behind using multiplication and not something else? Is it because this is 1/4 of the 2/5? 08:40 But it wouldn't hurt to show these formulas anyway, now when we know what hides behind them.
Imagine rectangle made of 5 smaller squares. If we asked to paint 2/5 of the rectangle, that means we paint 2 squares in it and leave 3 squares unpainted. Now suppose I said you to repaint 1/4 of the painted part. In order to do that, you split EVERY square in rectangle into 4 equal squares. Now you have more refined grid of 5 × 4 = 20 squares, so that you can measure parts of the rectangle more accurately. In that new grid 4 + 4 = 8 squares will be painted and 12 are unpainted. Now it is easy to perform repainting task. 1/4 out of 8 squares is 2 squares. If we look globally on the whole rectangle, we have 2 repainted squares, 8 painted squares (including repainted ones) and 12 unpainted squares. Did that help?
Охтеров Егор Yes. Actually I figured it out after watching several other videos, and it seems that my original intuition ("Is it because this is 1/4 of the 2/5?") was correct after all. I just couldn't find this comment again to leave an explanation for others (heh... search engine my ass... :P ). So thanks for your explanation, it will definitely help other people.
Excellent video! However in actual practice of medical diagnosis should we also not consider the physician is already suspecting one could have cancer based on symptoms? This example to me is analogous to running test on random people on the street. Or should I interpret the base rate actually indicates symptomatic rate i.e of 1000 people showing symptoms only 1 actually has cancer?
THINK YOU CAN ANSWER 2 QUESTIONS IN PROBABILITY THAT NOONE ELSE IN THE WORLD CAN? 1. Why is the formula (no. of favorable outcomes) / (total no. of outcomes) 2. Assuming that event A and B are both independent, why is P(A intersect B) = P(A)*P(B) Why do we use these formulae? Where is the derivation? How does it work? Where did it come from? (I meant "noone else" in my world, as in all the people that I've met and asked these questions to)
I'm not convinced that the probabiity that " the blue marvel was picked from A " depends on the number of blue marvels in each bowl , I think , given that the person knows that he must pick a blue marvel he wil be facing only two options, either he picks the blue marvel from the the bowl A or the bowl B. Therefore, and because these two options are equaly likely, the probabiity that the blue marvel is picked from the bowl A is one-half and not One out of four.
thankyou BUT the incidence rate in the population is irrelevant for the question asked which is what is the probability of you having cancer. without the test your probability is 0.001. BUT you have had the test so DISREGARD the population parameter the prob. you have the cancer is ~99%
Is these the same content were the math is fun article is based? They are almost exactly the same just different examples. Anyway another bad lesson on conditional probability, why do mathematicians focus a lot on the result and not the process.
This is an excellent course! The only thing that I could point is that at 7:30, it would have be better to use different outcomes for P(B1 and Y2), P(Y1 and B2) and P(Y1 and Y2). 3/10 for each can be a bit confusing, especially at 8:22.
This is a succinct and elucidatory video. The table and tree approaches are particularly useful for an old person like me who find it hard to keep things in our short term memory. An excellent video for me. Thank you!
Mr Sam, When the data is changed in the first example, it doesn't comply with the Bayes rule, something is wrong somewhere. Pl check. P(A/blue)= P(blue/A).P(A) ÷ [ P(blue/A).P(A) + P(blue/B).P(B)] Let changed data is bowl A has 3 blue and 7 yellow marbles. Bowl B has 5 blue and 11 yellow. As per your table method, P(A/blue)= 3/8. As per Bayes rule, P(A/blue)=24/49. Please clear the doubt. I have assumed P(A)=P(B)=1/2
I learned a lot from this video. However, I have a sense that there is something wrong. Did I miss something? Did Sam fail to emphasise something? At 2:03, Sam gives P(Blue)=4/10 and P(Yellow)=6/10. Those answers are correct, but his approach appears to be non-generic. Specifically, if we change the problem slightly, and make bowl A contain one less yellow marble (i.e., 1 blue marble and 3 yellow marbles), his approach gives wrong answers, viz., P(Blue)=4/9 and P(Yellow)=5/9. The problem consists of two stages: 1) Picking a bowl at random, and 2) Picking a marble at random from the bowl picked. Sam ignores the first stage altogether in his approach. Probability of picking bowl A or B is as follows: P(Bowl A) = P(Bowl B) = 1/2. P(Blue | Bowl A) = 1/4. P(Blue | Bowl B) = 3/5. P(Blue and Bowl A) = P(Bowl A) * P(Blue | Bowl A) = (1/2)*(1/4) = 1/8. P(Blue and Bowl B) = P(Bowl B) * P(Blue | Bowl B) = (1/2)*(3/5) = 3/10. P(Blue) = P(Blue and Bowl A) + P(Blue and Bowl B) = (1/8) + (3/10) = 17/40. Similarly, P(Yellow)=23/40.
But let's say I have 1 and only 1 marble in cup A, and it's a blue marble, and say 5 out of 11 marbles in cup B are blue marbles. It feels like if I know I picked a blue marble, then there should be more than a 1/6 chance of that marble coming from cup A. I guess because since cup A i this case is 100 percent blue? I don't know...
if i received a positive and the test was 99% accurate then i am not going to get excited jumping up and down. i would be organising my will and last farewells.
If suppose you add 2 blue marble in bowl 1 then what will be the probability of choosing marble from bowl 1? It looks that choosing marble from any bowl probability will be half but actually it is not...🤔
rarely i do comment on a video its that one i have trouble to understand those formula and implement them in question for 2 yrs . This is the video for which i search this topic in utube
Sam, you are a great teacher! Sample space is explained excellently, just by visualising. The cancer example emphazises that one should take the prevalence of cancer into account, interpretating the quality of a test positive result in patients who do not have the disease. I have never seen explaining the subject of conditional probability, so clearly,
that moment wen hours of study are cleared by a 12 minute video no wonder the MIT is number one wish i had 200k to spend in that college unfortunatelly poor scores and have no money... the bright side is that i can calculate the probs of getting there anyway thanks MIT
I spent over 5 days trying to figure out the given term. You are amazing! I finally under the conditional Probability. Thank you.
Amazing video. I have watched so many long videos about conditional probability.
This video is very dense, clear, and right on the point. I am going to watch the rest of the videos through this channel
No distraction...Check!
Clear explanations ...Check!
No memorisation required...Check!
Clear demonstrations...Check!
Excellent!
Great vid! Just a caveat for the viewers about the medical tests. He forgot to mention he was specifically talking about screening tests for rare but horrible diseases in the general population. Normally when your doctor orders a test, your prior probability is a lot higher than the prevalence in the general population. Let's say because you have symptoms fitting the disease, your prior is 1 in 10 instead of 1 in 1000. Now the test is suddenly very useful. By testing positive, you go from 10% to 92% probability of having the disease.
I watched this video about 5 times with brakes for exercises and finally understand! Great, thanks!!
3/5(yellow balls in bowl B from scope A&B) * 2/5 (1st ball is blue) * 5/3 (divide by % of 1st ball is yellow) = 1/2
Thank you! I have watched many other videos and could not grasp the essence of differentiating P(A|B) from P(B|A). Your example was practical and clear. :)
My lecturer *for this subject* isn’t bad at explanation, but this is so easy to learn and understand
Oh my god you have cleared my mind here !!! :D
no word for this explanation it shows best students makes institute best
I did that in high school for my Cambridge University Int Examination Mathematics A level
Just let me say THANK YOU! MIT
one of the best video for conditional video
Bayes theorem is a formulation of conditional probability
Amazing explanation! Thank you very much ... if we consider this problem with the same setting, the accuracy of the test need to be around .99999% instead of .99% to achieve .99% of accuracy in the real world! Now I have a more clear understanding why is so difficult to introduce a machine (i.e a deep learning system that analyses histology slides) that makes a clinical diagnosis in the real world.
Amazing one. Now, I can understand basic topics of Information Theory and Coding and Communication Systems lectures well. No more Bayes'' rule and facepalm. :D
This video shows how good teaching at MIT must be, and how good the students are too.
I have a doubt.Why do we multiply the probabilities of Blue marble and Blue marble in the tree diagram while we perform a summation - p(b1&y2)+p(y1&y2) to arrive at p(y2)?
Bro you have really good thinkimg level .
will you make best problems on calculus
very good presentation of conditional probability!!! clears lot of mud
I was so confused about this topic,bit this helps a lot.
I didn't understand until I watched the practical medical example. More real world examples in math please.
I have a doubt. I am confused as to why are we able to multiple the probabilities in the cases of P(B1 and B2), P(B1 and Y1) etc. If we are NOT doing replacement, the events are dependent on each other. And the multiplication rule applied to independent events only right?
Can someone help?
This is a good video, nice and clear and perfectly illustrated! THUMBS UP!
06:40 Why do we _multiply_ them? What's the reasoning behind using multiplication and not something else? Is it because this is 1/4 of the 2/5?
08:40 But it wouldn't hurt to show these formulas anyway, now when we know what hides behind them.
Imagine rectangle made of 5 smaller squares. If we asked to paint 2/5 of the rectangle, that means we paint 2 squares in it and leave 3 squares unpainted. Now suppose I said you to repaint 1/4 of the painted part. In order to do that, you split EVERY square in rectangle into 4 equal squares. Now you have more refined grid of 5 × 4 = 20 squares, so that you can measure parts of the rectangle more accurately. In that new grid 4 + 4 = 8 squares will be painted and 12 are unpainted. Now it is easy to perform repainting task. 1/4 out of 8 squares is 2 squares. If we look globally on the whole rectangle, we have 2 repainted squares, 8 painted squares (including repainted ones) and 12 unpainted squares.
Did that help?
Охтеров Егор Yes. Actually I figured it out after watching several other videos, and it seems that my original intuition ("Is it because this is 1/4 of the 2/5?") was correct after all. I just couldn't find this comment again to leave an explanation for others (heh... search engine my ass... :P ). So thanks for your explanation, it will definitely help other people.
Excellent video! However in actual practice of medical diagnosis should we also not consider the physician is already suspecting one could have cancer based on symptoms? This example to me is analogous to running test on random people on the street. Or should I interpret the base rate actually indicates symptomatic rate i.e of 1000 people showing symptoms only 1 actually has cancer?
Yes, you are correct. The analysis in the video assumes that the given base rate is for the population that the person is drawn from.
THINK YOU CAN ANSWER 2 QUESTIONS IN PROBABILITY THAT NOONE ELSE IN THE WORLD CAN?
1. Why is the formula (no. of favorable outcomes) / (total no. of outcomes)
2. Assuming that event A and B are both independent, why is P(A intersect B) = P(A)*P(B)
Why do we use these formulae? Where is the derivation? How does it work? Where did it come from?
(I meant "noone else" in my world, as in all the people that I've met and asked these questions to)
Wayfair you got just what I need!
me: Ah yes lets study some probability
MIT: you've got cancer now
This is good to watch for my Egzam
Awesome video.
Thanks MIT.
Clear explanation! Thank you
Thank you very much sir , thank you .............................
Excellant! Now i will never use Bayes theorem. I will do it this way only.
+akshay padmanabhan Curious... Why would stop using Bayes' Theorem?
After watching this video i really familiar from c prop..Thx
Thanku very much sir u save my life
Very helpful , thank you, have a great day,, 😚,
really simplified ... thanks...
You are the best.
thanks a lot
Nice Explanation :)
this kid looks just as dead inside as i am.
THANK YOU SIR!!!
very well explained! thank you :)
this is great
jenius explained
really helpful
Conditional probability restricts the sample space
thanks sir realy hope me alot
8:32 didn't get that
awesomely crazy
I'm not convinced that the probabiity that " the blue marvel was picked from A " depends on the number of blue marvels in each bowl , I think , given that the person knows that he must pick a blue marvel he wil be facing only two options, either he picks the blue marvel from the the bowl A or the bowl B. Therefore, and because these two options are equaly likely, the probabiity that the blue marvel is picked from the bowl A is one-half and not One out of four.
nice video bro
This guy now has Ph.D. in Maths. Jeez I envy your brain man.
i’m still pausing the video
thankyou BUT
the incidence rate in the population is irrelevant for the question asked which is what is the probability of you having cancer.
without the test your probability is 0.001. BUT you have had the test so DISREGARD the population parameter
the prob. you have the cancer is ~99%
how to survive cancer using maths 101
Is these the same content were the math is fun article is based? They are almost exactly the same just different examples. Anyway another bad lesson on conditional probability, why do mathematicians focus a lot on the result and not the process.
The video seems to have cut off the last number (.01) in the numerator of the caclulation of P(cancer | test +) at 10:58
This is an excellent course! The only thing that I could point is that at 7:30, it would have be better to use different outcomes for P(B1 and Y2), P(Y1 and B2) and P(Y1 and Y2). 3/10 for each can be a bit confusing, especially at 8:22.
yea i can't understand what he did at 8:22 , can you explain?
You multiply the two fractions on the same arm and will get it
@@xtuki2150 it's bayes theorem!
Thank you for question Tsunami! :o and for the answer Bel Zhang
@@xtuki2150 it's (2/5+3/4)÷((2/5x3/4)+(3/5x2/4)) =0.5
OMG this is amazing
This is a succinct and elucidatory video. The table and tree approaches are particularly useful for an old person like me who find it hard to keep things in our short term memory. An excellent video for me. Thank you!
Sam Watson, start your own UA-cam channel! This is so easy to understand! Finally my marbles fell in the right places :p
That could not have been any clearer. Thank you MIT and thank you Sam.
Cool video, never knew about the tree diagram before this. Very useful in finding out the probability of the same thing twice.
The example ending at 08:33 is not clear for me. Why the possible outcomes are 3/10 + 3/10 there?
That's the probablity of yellow coming at second ..
Given as : P(Y2) = P(B1 and Y2) + P(Y1 and Y2) = 3/10 + 3/10 ..
Marc C watch till end you will understand everything. By watching real world example.
would you elaborate that inequality @11:32 ?
awesomeeeee could not get any clearer than this! and i've seen several! THANKS
Help
the video is cut off on the sides
Ohh , so this is MIT from where Havord got his MTECH degree !!
the concept of tree diagrams makes it so easy to visualize. Thank you
i have watched many times this video,but nthing i understood
Thank you so much. Simplified and made easy.
as the famous actor always says:
WOW!!
Owen Wilson, right? 😁
I need a small conversation with you. Please help me on understanding the probability problems.
why i am so stupid?
U r not
Thanks, this is a top tier video!
This is absolutely the clearest explanation of conditional probability I have ever seen.
Mr Sam,
When the data is changed in the first example, it doesn't comply with the Bayes rule, something is wrong somewhere. Pl check.
P(A/blue)= P(blue/A).P(A) ÷ [ P(blue/A).P(A) + P(blue/B).P(B)]
Let changed data is bowl A has 3 blue and 7 yellow marbles.
Bowl B has 5 blue and 11 yellow.
As per your table method, P(A/blue)= 3/8.
As per Bayes rule,
P(A/blue)=24/49.
Please clear the doubt.
I have assumed P(A)=P(B)=1/2
Amazing Demonstration ...finally got some idea.
I learned a lot from this video. However, I have a sense that there is something wrong. Did I miss something? Did Sam fail to emphasise something?
At 2:03, Sam gives P(Blue)=4/10 and P(Yellow)=6/10. Those answers are correct, but his approach appears to be non-generic. Specifically, if we change the problem slightly, and make bowl A contain one less yellow marble (i.e., 1 blue marble and 3 yellow marbles), his approach gives wrong answers, viz., P(Blue)=4/9 and P(Yellow)=5/9.
The problem consists of two stages: 1) Picking a bowl at random, and 2) Picking a marble at random from the bowl picked. Sam ignores the first stage altogether in his approach.
Probability of picking bowl A or B is as follows: P(Bowl A) = P(Bowl B) = 1/2. P(Blue | Bowl A) = 1/4.
P(Blue | Bowl B) = 3/5.
P(Blue and Bowl A) = P(Bowl A) * P(Blue | Bowl A) = (1/2)*(1/4) = 1/8.
P(Blue and Bowl B) = P(Bowl B) * P(Blue | Bowl B) = (1/2)*(3/5) = 3/10. P(Blue) = P(Blue and Bowl A) + P(Blue and Bowl B) = (1/8) + (3/10) = 17/40. Similarly, P(Yellow)=23/40.
Excellent teaching.. easiest way to solve conditional problem
*opens video* you have been tested positive for a deadly cancer.. @.@
But let's say I have 1 and only 1 marble in cup A, and it's a blue marble, and say 5 out of 11 marbles in cup B are blue marbles. It feels like if I know I picked a blue marble, then there should be more than a 1/6 chance of that marble coming from cup A. I guess because since cup A i this case is 100 percent blue? I don't know...
Why does the probability of having cancer is 1/1000 or .001? Where's the thousand came from? Thanks.
if i received a positive and the test was 99% accurate then i am not going to get excited jumping up and down. i would be organising my will and last farewells.
Someone show this to CNN for calling about more testing everyday
At 4:06, i get different result for P(A/blue) using Bayes rule. can any one tell why Bayes rule not used here?
can someone clear my doubt? since the blue marvel was drawn first. Will the probability depend on 2nd marvel being yellow or blue? 8:30
If suppose you add 2 blue marble in bowl 1 then what will be the probability of choosing marble from bowl 1? It looks that choosing marble from any bowl probability will be half but actually it is not...🤔
awesome video ,too much to suck in at once :O
Do the odds change with social distancing?
rarely i do comment on a video its that one
i have trouble to understand those formula and implement them in question for 2 yrs . This is the video for which i search this topic in utube
Sam, you are a great teacher!
Sample space is explained excellently, just by visualising.
The cancer example emphazises that one should take the prevalence of cancer into account, interpretating the quality of a test positive result in patients who do not have the disease.
I have never seen explaining the subject of conditional probability, so clearly,
Sir will you please make more videos on probability
School in maths : i will bore u
Utube in maths : it is damm intresting
You go slow during the easy parts and too fast when its gets tricky. I had to rewind many times
good lecture
Thanks for this. It's cute because you talk like an AI