Question

question 6 of 25
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. 0.08
b. 0.17
c. 0.32
d. 0.22

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that the vehicle is white and \(B\) be the event that the vehicle is a car.

Step2: Substitute the given values into the formula

We are given that \(P(A) = 0.25\), \(P(B)=0.36\), and \(P(A\cap B) = 0.08\). Using the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), we substitute \(P(A\cap B) = 0.08\) and \(P(B)=0.36\) into it. So \(P(A|B)=\frac{0.08}{0.36}\).

Step3: Calculate the value

\(\frac{0.08}{0.36}=\frac{8}{36}=\frac{2}{9}\approx0.22\) (rounded to two decimal places).

Answer:

D. 0.22