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.
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
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.
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.
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!
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
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.
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%
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?
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 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...🤔
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.
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.
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,
isn't there an error in the last calculation regarding probability of cancer? denominator after + sign should be ...... (.999 x .01) ---- not just + (.999) ??
Because that is proportion of Yellow second (when you want to calculate propotion of Blue first with condition is yelllow second you must take propotion of blue first divide proportion of yellow second), i wish this useful with you.😀
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)
Every outcome is equally likely. So you just find how many total outcomes there are. How many outcomes your criteria fits, and the probability of the event will be the no. Of outcomes the criteria fits over the total number of outcome
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. :)
I watched this video about 5 times with brakes for exercises and finally understand! Great, thanks!!
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.
really simplified ... thanks...
this is great
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
The video seems to have cut off the last number (.01) in the numerator of the caclulation of P(cancer | test +) at 10:58
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
Oh my god you have cleared my mind here !!! :D
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
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 spent over 5 days trying to figure out the given term. You are amazing! I finally under the conditional Probability. Thank you.
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!
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
Sam Watson, start your own RUclips 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.
OMG this is amazing
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 ?
this kid looks just as dead inside as i am.
No distraction...Check!
Clear explanations ...Check!
No memorisation required...Check!
Clear demonstrations...Check!
Excellent!
I need a small conversation with you. Please help me on understanding the probability problems.
Bro you have really good thinkimg level .
will you make best problems on calculus
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
awesomeeeee could not get any clearer than this! and i've seen several! THANKS
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.
i have watched many times this video,but nthing i understood
as the famous actor always says:
WOW!!
Owen Wilson, right? 😁
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%
My lecturer *for this subject* isn’t bad at explanation, but this is so easy to learn and understand
the concept of tree diagrams makes it so easy to visualize. Thank you
Ohh , so this is MIT from where Havord got his MTECH degree !!
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)?
Why does the probability of having cancer is 1/1000 or .001? Where's the thousand came from? Thanks.
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?
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...
Just let me say THANK YOU! MIT
Thank you so much. Simplified and made easy.
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...🤔
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
the video is cut off on the sides
me: Ah yes lets study some probability
MIT: you've got cancer now
At 4:06, i get different result for P(A/blue) using Bayes rule. can any one tell why Bayes rule not used here?
This is absolutely the clearest explanation of conditional probability I have ever seen.
*opens video* you have been tested positive for a deadly cancer.. @.@
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.
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.
Someone show this to CNN for calling about more testing everyday
Excellent teaching.. easiest way to solve conditional problem
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
I did that in high school for my Cambridge University Int Examination Mathematics A level
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,
You go slow during the easy parts and too fast when its gets tricky. I had to rewind many times
Help
isn't there an error in the last calculation regarding probability of cancer? denominator after + sign should be ...... (.999 x .01) ---- not just + (.999) ??
It's there it just didn't show up on the screen.
Thanks, this is a top tier video!
School in maths : i will bore u
Utube in maths : it is damm intresting
Amazing Demonstration ...finally got some idea.
Thanks for this. It's cute because you talk like an AI
why i am so stupid?
U r not
Very helpful , thank you, have a great day,, 😚,
Sir will you please make more videos on probability
Explain from 8:31 cant understand why 3/10+3/10 ?????
Because that is proportion of Yellow second (when you want to calculate propotion of Blue first with condition is yelllow second you must take propotion of blue first divide proportion of yellow second), i wish this useful with you.😀
awesome video ,too much to suck in at once :O
one of the best video for conditional video
how to survive cancer using maths 101
Wayfair you got just what I need!
This is a good video, nice and clear and perfectly illustrated! THUMBS UP!
Do the odds change with social distancing?
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)
good lecture
i’m still pausing the video
11:25 Accuracy is defined as (true positives + true negatives) / (true positives + true negatives + false positives + false negatives). Shouldn't it be P(test postive | cancer) + P(test negative | ¬cancer)?
Every outcome is equally likely. So you just find how many total outcomes there are. How many outcomes your criteria fits, and the probability of the event will be the no. Of outcomes the criteria fits over the total number of outcome
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
Tree Diagram: The best soln to conditional probability, law of total probability, Bayes theorem
Damnnn! I come on here and the first thing I hear is you have tested postive for a deadly cancer. Sheesh. Can we get a happier problem.
Excellent, thank you
nice explanation...How tree diagram should be made for P(A/blue)?
Sets and Probability is the basics of flexible thinking and reasoning. What a topic
I didn't understand until I watched the practical medical example. More real world examples in math please.
Nice Explanation :)
the cancer problem does not work with a grid. How to decide whether to use the tree diagram or the grid when starting out with a problem?
What is MATHEMATICS!!!!!!!
very good presentation of conditional probability!!! clears lot of mud
شرحك رائع.
استمر
This guy now has Ph.D. in Maths. Jeez I envy your brain man.
After watching this video i really familiar from c prop..Thx
thanks for helping me understand probability without the bayes theorem
This is good to watch for my Egzam
thank you , I finally understood after watching hundreds of videos....
Trees are so easy
Dammnn, they tell us some wierd formulae for that
Loved it
Wonderful video.
1:29 these are distinct events
This video shows how good teaching at MIT must be, and how good the students are too.
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. :)
very informative with methods that are straightforward to grasp.
Bayes theorem is a formulation of conditional probability
Thanks for the upload. Found it really useful1
I was so confused about this topic,bit this helps a lot.
Conditional probability restricts the sample space