Question

New car: At a certain car dealership, the probability that a customer purchases an SUV is . Given that a customer purchases an SUV, the probability that it is black is . What is the probability that a customer purchases a black SUV? Round your answer to four decimal places, if necessary.

Answer 1

0.05 is the probability that a customer purchases a black SUV.

Explanation:

The following information is missing in the question:

"At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25."

We are given the following in the question:

Probability a customer buys a SUV = 0.20

`P(S) = 0.20`

Probability that the SUV is black, given customer purchases a SUV = 0.25

`P(B|S) = 0.25`

We have to find the probability that a customer purchases a black SUV.

Thus, we have to evaluate:

`P(B\cap S)`

Formula for conditional probability:

`P(B|S) = (P(B\cap S))/(P(S))\\\\P(B\cap S) = P(B|S)* P(S) = 0.25* 0.20 = 0.05`

0.05 is the probability that a customer purchases a black SUV.