Conditional Probability Example Problems

Conditional probability example problems, pitched at a level appropriate for a typical introductory statistics course. I assume that viewers have already been introduced to the concepts of conditional probability and independence, but I do review the concepts along the way. I work through some problems with the conditional probability formula explicitly, and some using the reduced sample space argument.

The sudden death data is slightly modified from:

Naneix et al. (2015). Sudden adult death: An autopsy series of 534 cases with gender and control comparison. Journal of Forensic and Legal Medicine, 32:10-15.

The data was pulled from their Figure 3, and I pooled the Abdominal/pelvian and undetermined groups into "other", to make the example work better visually and have it be easier to follow. I took some slight liberties here, as "undetermined" is not the same as "other". Conscious choice, y'all.

Examples:

0:58. An example using the conditional probability formula, where we are given P(A), P(B), and P(A U B).

3:06: Die rolling. Everybody's fave. P(AUB|C).

4:51. Two-way table, involving real data from above. Limited on interpretation, and focussing on finding various conditional probabilities.

8:05. Conditional probability involving 3 events, visualized with a Venn diagram. P(A n C | B n C), P(B^c|A U C).

11:21. Example of determining whether P(A|B) = P(A), P(A|B) is less than P(A), or P(A|B) is greater than P(A), based on common knowledge and without being given probabilities.

13:00. Informal illustration that if P(A|B) is greater than P(A) then P(B|A) is greater than P(B), and if P(A|B) is less than P(A) then P(B|A) is less than P(B).

14:40. If A is a subset of B, and P(A) is greater than 0, what can be said of P(A|B) and P(B|A)?

[carlosdominguez]

By far, this is the best explanation I have seen of this topic. Congratulations!

[barrowmeoct]

Thank you, this has made it so much easier. I only wish I had discovered your videos on this months earlier. This has made understanding the probability trees much much easier as well. As someone else has stated here, this really demystified things in terms of understanding what you are actually trying to figure out.

[emmaaye]

thanks so much. I was having hard time understanding conditional probability of 3 variables. I have searched web and this is so far clearest way to understand

[paradox]

Thank you so much for this video! I'm preparing for an electrical communications theory course for next semester and I need to brush up on my probability theory. This is such an incredibly helpful resource you've put together.

[richmertl]

Haha, Professor I love the subtle way you let on that you haven't been to a party in recent memory! If you are ever coming to New York City where I live, let me know and it will be my treat to take you out for a night on the town 😀

[Maha_s]

YAY!!! Prof Balka is back! So exicited. Happy New Year Prof!

[NexusEight]

Good job on the visualisations of the conditional probabilities with the Venn Diagrams!

[waykelly]

one of the best videos i watched 2020 so far as per my course is concerned

[andres]

What's up with the party part at the end? Mmm. I must be out of touch with the modern era?

[moon-coder]

Why you did not want to write/say at 16:12 that P(A|B)=P(A)/P(B) ?

[tatai]

How do you prove the part P(A∪B|C) using conditional probability formulae?

[michelravenespinoza]

Finally. Found the video ive been looking for

[arielleariella]

At 8:02 if you add the probabilities of males dying given the cause was cerebral or respiratory separately you get a value bigger than 1....but if combine them like it was done in the video you get 0.569. Shouldn't they give you the same answer?

[sarahkitner]

How do I know when to apply the probability formula and when I want to apply reduced sample space method?

[lamborghiniveneno]

This is the Best explaination I ever came across!!!

[minhtamnguyen]

Thankyou so much for making this video. I just bing-watching some of your videos about probability and all of them are great <333

[magiquemarker]

At @9:04, where did the 0.30 outside of the three circles come from???

[kantorghor]

There is something off at 11:11 why not B is 0.41 instead of 0.71 (1-P(B)=0.71), i probably didn't get the notation.
Thanks for the video.

[bleepbloop]

at 2:58 it says P(AnB) is = 0.14 but I got 0.20 when I solved it, which also equals 0.70...why is my answer different here?

[hareeshd]

@jbstatistics, Someone please help...
At 10:45 p(A U C) = p(A)+p(B)-p(A intersection C) denominator
Shouldn't we write like this ???