Question

A survey finds that 48% of people identify themselves as fans of professional football, 12% as fans of car racing, and 9% as fans of both professional football and car racing. Let event F be choosing a person who is a fan of professional football and let event C be choosing a person who is a fan of car racing.

Which statements are true? Select three options.

P(F|C) = 0.75
P(C|F) = 0.25
P(C∩F) = 0.09
P(C∩F) = P(F∩C)
P(C|F) = P(F|C)

Answer 1

The true statements are:

- P(F|C) = 0.75 (0.09/0.12 = 0.75)
- P(C∩F) = 0.09 (given)
- P(C∩F) = P(F∩C) (intersection is symmetric)

The others are false: P(C|F) = 0.09/0.48 = 0.1875 (not 0.25), so P(C|F) ≠ P(F|C).