Conditional Probability
ฝัง
- เผยแพร่เมื่อ 28 พ.ค. 2024
- MIT RES.TLL-004 Concept Vignettes
View the complete course: ocw.mit.edu/RES-TLL-004F13
Instructor: Sam Watson
This video provides an introduction to conditional probability and its calculations, as well as how it can be used to interpret medical diagnoses.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
I watched this video about 5 times with brakes for exercises and finally understand! Great, thanks!!
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
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!
That could not have been any clearer. Thank you MIT and thank you Sam.
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 absolutely the clearest explanation of conditional probability I have ever seen.
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 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.
the concept of tree diagrams makes it so easy to visualize. Thank you
Cool video, never knew about the tree diagram before this. Very useful in finding out the probability of the same thing twice.
Sets and Probability is the basics of flexible thinking and reasoning. What a topic
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. :)
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,
Sam Watson, start your own TH-cam channel! This is so easy to understand! Finally my marbles fell in the right places :p
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
Thank you so much for this class! I've been struggling with conditional probabilities for weeks. Now everything's so much clear!
no word for this explanation it shows best students makes institute best
Thank you so much. Simplified and made easy.
awesomeeeee could not get any clearer than this! and i've seen several! THANKS
The most thought provoking video on you tube
very informative with methods that are straightforward to grasp.
Oh my god you have cleared my mind here !!! :D
My lecturer *for this subject* isn’t bad at explanation, but this is so easy to learn and understand
very good presentation of conditional probability!!! clears lot of mud
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 finally understood after watching hundreds of videos....
Amazing Demonstration ...finally got some idea.
Excellent teaching.. easiest way to solve conditional problem
one of the best video for conditional video
Awesome video.
Thanks MIT.
Thank you for an amazing video. Really helpful
WOW. such an insightful video.
Just let me say THANK YOU! MIT
good illustration with the tree. Bravo
Clear explanation! Thank you
Thanks, this is a top tier video!
incredible, i can't imagine better teaching
crystal clear explaination .. thanks a lot for that.
crystal clear explanation...thanks a lot
This is a good video, nice and clear and perfectly illustrated! THUMBS UP!
Fantastic video easily understood the concept :)
I was so confused about this topic,bit this helps a lot.
Great explanation
OMG this is amazing
This video shows how good teaching at MIT must be, and how good the students are too.
Wayfair you got just what I need!
Wonderful video.
Thank you for your amazing explanation :)
This is a really amazing video.. wow..
I did that in high school for my Cambridge University Int Examination Mathematics A level
This is an amazing video .. Thanks so much
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
Very good Bayes refresher.
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.
Thanks for the upload. Found it really useful1
Bro you have really good thinkimg level .
will you make best problems on calculus
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
nice explanation...How tree diagram should be made for P(A/blue)?
Excellent, thank you
thanks for helping me understand probability without the bayes theorem
Thank you! It's a very obvious video!!
At 4:06, i get different result for P(A/blue) using Bayes rule. can any one tell why Bayes rule not used here?
Amazing Video
very well explained! thank you :)
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.
This is good to watch for my Egzam
Thanks Sam.
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
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?
Thank you very much sir , thank you .............................
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
Thank you my man
Awesome! Thanks so much
really simplified ... thanks...
Bayes theorem is a formulation of conditional probability
I need a small conversation with you. Please help me on understanding the probability problems.
THANK YOU SIR!!!
awsome video
Very well done. Thank you. I think I get it.
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)?
You are the best.
I didn't understand until I watched the practical medical example. More real world examples in math please.
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
good lecture
Nice Explanation :)
Sir will you please make more videos on probability
the video is cut off on the sides
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?
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...🤔
really cool one.
me: Ah yes lets study some probability
MIT: you've got cancer now
Excellent
hats off man..!
well done!
Thanku very much sir u save my life
jenius explained
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)?
this is great