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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)

Respuesta :

JeanaShupp

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

[tex]P(F\cap C)=P(C\cap F)=9\%=0.09[/tex]

Now, [tex]P(F|C)=\dfrac{P(F\cap C)}{P(C)}=\dfrac{0.09}{0.12}=0.75[/tex]

[tex]P(C|F)=\dfrac{P(C\cap F)}{P(F)}=\dfrac{0.09}{0.48}=0.1875[/tex]

Parrain

Based on the given probabilities, the following are true:

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

Assume that F is for the probability that a person is a fan of football and C is for fans of car racing.

Calculating the probabilities

P(F|C) = P(F∩C) / P (C)

= 0.09 / 0.12

= 0.75

P(F∩C) is the same as P(C∩F). P(C∩F) is therefore 0.09 or 9%.

Find out more on probability at https://brainly.com/question/19349840.

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