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)?