Fall 2011 Homework 3: Question 3
Is it possible to have events $A_{1}, A_{2}, B, C$ with $P(A_{1}|B)>P(A_{1}|C)$ and $P(A_{2}|B)>P(A_{2}|C)$, yet $P(A_{1} \cup A_{2}|B)>P(A_{1}\cup A_{2} |C)$? If so, find an example (with a "story" interpreting the events, as well as giving specific numbers); otherwise, show that it is impossible for this phenomenon to happen.
Solution: Yes, this is possible. Consult iTunes course for full solution, with an example of a streaky basketball player and a more consistent player and an example of Good Class and Other Class.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."