Reading Quiz 3 Solutions
1. P(A|B) is larger. It is likely that most, if not all, American soccer players who played soccer in the Olympics also played soccer in high school. Therefore, given that a person played soccer in the Olympics, the probability that the person played soccer in high school is very large.
Alternative explanation: P(B) is likely to be much smaller than P(A) because the number of American adults that have played soccer in the Olympics is much smaller than the number that have played soccer in high school. P(A|B)=P(A and B)/P(B) and P(B|A)=P(A and B)/P(A). Since P(B) is much smaller than P(A), P(A|B) is going to be bigger than P(B|A).
(Your explanation didn't need to be this detailed. We provide this merely to help you understand the solution.)
2. P(F|E)
3. Thank you for your feedback and comments.