Question

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

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

Explanation:

The question is incomplete:

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.

The probability that a customer purchases a black SUV can be calculated as the multiplication of this 2 factors:

• The probability of a customer purchasing a SUV: P(SUV).
• The probability that it is black, given that he or she purchases a SUV (conditional probabilty): P(B|SUV)

We know then:

`P(SUV)=0.25\\\\P(B | SUV)=0.20`

We can now calculate the probability as:

`P(B\,\&\,SUV)=P(B|SUV)\cdot P(SUV)=0.25\cdot0.20=0.05`