(8 points) At a certain auto dealership, there are cars and SUVs sold. The proba

Question

(8 points) At a certain auto dealership, there are cars and SUVs sold. The probability that a randomly selected customer will purchase an SUV is 35%. The probability that a randomly selected customer will purchase a car is 65%. If the customer purchases an SUV, there is a 50% probability it will be black. If the customer purchases a car there is a 10% probability that it will be black. Define the events

C = event that a car is purchased

S = event that a SUV is purchased

B = event that a black vehicle is purchased

If a randomly selected customer has purchased a black vehicle, what is the probability that it is a car?

Explanation / Answer

We need to calculate

P( Car/Black)

P( black) = 0.35*0.50+0.65*0.10 = 0.24

P( Car/Black) = (0.65*0.10)/0.24 = 0.2708 ( Rounded to four decimal places)

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