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? Check all that apply.


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

1. P(F|C) = 0.75

3. P(C∩F) = 0.09

4. P(C∩F) = P(F∩C)

Answer 2

Answer: P(F|C) = 0.75

P(C∩F) = 0.09

P(C∩F) = P(F∩C)

Step-by-step explanation:

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.

By the given information we have:

P(F)=48%=0.48

P(C)=12%=0.12

$P(F\cap C)=P(C\cap F)=9\%=0.09$

Now, $P(F|C)=\dfrac{P(F\cap C)}{P(C)}=\dfrac{0.09}{0.12}=0.75$

$P(C|F)=\dfrac{P(C\cap F)}{P(F)}=\dfrac{0.09}{0.48}=0.1875$