Question

the accompanying table shows the number of cars of two different brands sold at a dealership during a certain month. the number of coupes and sedans is also shown. if one of these vehicles is selected at random, determine the probability that the vehicle was brand 2, given that the vehicle selected was a coupe. the probability that a vehicle was brand 2, given that the vehicle was a coupe, is (round to four decimal places as needed.)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of this problem, if \(A\) is the event that the vehicle is Brand 2 and \(B\) is the event that the vehicle is a coupe, then \(P(A|B)=\frac{\text{Number of Brand 2 coupes}}{\text{Total number of coupes}}\).

Step2: Identify the relevant values from the table

From the table, the number of Brand 2 coupes is \(255\), and the total number of coupes is \(350\).

Step3: Calculate the probability

Substitute the values into the formula: \(P=\frac{255}{350}\approx0.7286\)

Answer:

\(0.7286\)