Question

A video game randomly chooses your car color and type. The probability of

getting a red car is 0.20, and the probability of getting a convertible is 0.40.
Event A = You
get a red car.
Event B = You get a convertible.
A and B are independent events if

A. The probability of getting a red car or a convertible is 0.08

B. The probability of getting a red car or a convertible is 0.60

C. The probability of getting a red convertible is 0.08

D. The probability of getting a red convertible is 0

Answer 1

C. The probability of getting a red convertible is 0.08.

Explanation:

Given P(A) = 0.20 = probability of getting a red car, and P(B) = 0.40 = probability of getting a convertible, you want to know the conditions under which A and B are independent events.

Independent events

The conditional probability formula is ...

P(A|B) = P(A&B)/P(B)

This can be rearranged to ...

P(A&B) = P(A|B)·P(B)

If events A and B are independent, then P(A|B) = P(A). That means ...

P(A&B) = P(A)·P(B) . . . . . . when A and B are independent

P(red convertible) = P(red)·P(convertible) = 0.20·0.40 = 0.08

A and B are independent if ...

C. The probability of getting a red convertible is 0.08.

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