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

Answer:

P(F/C) = 0.75

P(C^F) = 0.09

P(C^F) = P(F^C)

Step-by-step explanation:

P(C^F) = 9% = 0.09

P(C^F) = P(F^C)

P(F/C) = P(F^C)/P(C)

= 0.09/0.12 = 0.75

Answer 2

The statements which are true are as follows:

1)  $P(F[C) = 0.75$

2) P(C∩F) = 0.09

3) P(C∩F) = P(F∩C)

What is Union and Intersection of sets?

'The union of two sets X and Y is defined as the set of elements that are included either in the set X or set Y, or both X and Y.

The intersection of two sets X and Y is defined as the set of elements that belongs to both sets X and Y.'

According to the given problem,

$P(F[C) =$  P(F∩C)/ P(C)

             = $\frac{0.09}{0.12}$

             = 0.75

P(C∩F) = 9%

            0.09

P(C∩F) = P(F∩C)

Hence, we can conclude that statements 1 , 3 and 4 are true.

Learn more about union and intersection of sets here:

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