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 \cap f) = 0.09\\)
\\(p(c \cap f) = p(f \cap c)\\)
\\(p(c|f) = p(f|c)\\)

Explanation:

Identify the given probabilities

Using the Probability Notation knowledge point

$$
LATEXBLOCK0
$$

Evaluate intersection statements

Using the Union and Intersection of Events knowledge point

$$
LATEXBLOCK1
$$

Calculate conditional probabilities

Using the Conditional Probability Calculation knowledge point

$$
LATEXBLOCK2
$$

Select the true statements

The three true statements are:

1. \(P(F|C) = 0.75\)
2. \(P(C \cap F) = 0.09\)
3. \(P(C \cap F) = P(F \cap C)\\)

Answer:

• **

$$P(F|C) = 0.75$$

(Correct answer)**
*

$$P(C|F) = 0.25$$

• **

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

(Correct answer)**

• **

$$P(C \cap F) = P(F \cap C)$$

(Correct answer)**
*

$$P(C|F) = P(F|C)$$