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 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, 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,
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 lesson is amazing! It's something every person should know about it because it gives you the ability to call the correct decision for your life, despite the matter is an illness or not.
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. :)
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.
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
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
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
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
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.
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)?
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)
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?
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.
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...🤔
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?
isn't there an error in the last calculation regarding probability of cancer? denominator after + sign should be ...... (.999 x .01) ---- not just + (.999) ??
Why isn't the Conditional Probability for P(A/Blue)= 1/2? I mean, there's two bowls, from each of which you could probably draw from. I'd really appreciate an explanation. Thank you in advance
Because the notation P (A|blue) has a different meaning i.e probability of drawing a marble from bowl- A GIVEN that its a blue one. Since we are dealing with blue marbles total blue marbles =4 (1 from A and 3 from B) now out of these 4 blue marbles the probability of drawing it from A is 1/4.
