At a car and truck dealership, the probability that a vehicle is white is 0.25. The probability that it is a car is 0.36. The probability that it is a white car is 0.08.What is the probability that a vehicle is white, given that the vehicle is a car? Round your answer to two decimal places.A.0.22B.0.08C.0.17D.0.32
Question
At a car and truck dealership, the probability that a vehicle is white is 0.25. The probability that it is a car is 0.36. The probability that it is a white car is 0.08.What is the probability that a vehicle is white, given that the vehicle is a car? Round your answer to two decimal places.A.0.22B.0.08C.0.17D.0.32
Solution
The probability that a vehicle is white, given that the vehicle is a car, is calculated using the formula for conditional probability. The formula is P(A|B) = P(A ∩ B) / P(B), where A is the event that the vehicle is white and B is the event that the vehicle is a car.
From the question, we know that: P(A) = Probability that a vehicle is white = 0.25 P(B) = Probability that it is a car = 0.36 P(A ∩ B) = Probability that it is a white car = 0.08
Substituting these values into the formula, we get:
P(A|B) = P(A ∩ B) / P(B) = 0.08 / 0.36 = 0.2222
Rounding to two decimal places, the probability that a vehicle is white, given that the vehicle is a car, is 0.22. So, the answer is A.0.22.
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