Question

a study found that 23% of the cars manufactured last year were suvs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white suvs. to the nearest whole percent, what is the probability that a car is an suv, given that it is white? 9% 15% 21% 57%

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 a car is an SUV and \(B\) be the event that a car is white. Then \(P(A\cap B)\) is the probability that a car is a white SUV, and \(P(B)\) is the probability that a car is white.

Step2: Substitute the given values into the formula

We are given that \(P(A\cap B) = 0.02\) (since \(2\%=0.02\)) and \(P(B)=0.13\) (since \(13\% = 0.13\)).
So \(P(A|B)=\frac{0.02}{0.13}\)

Step3: Calculate the value

\(\frac{0.02}{0.13}\approx0.1538\)

Step4: Convert to a percentage

\(0.1538\times100\% = 15.38\%\)

Answer:

\(15\%\) (Option 2)