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% 57% 21%

Explanation:

Step1: Recall the conditional probability formula

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. We are given \(P(A) = 0.23\), \(P(B)=0.13\), and \(P(A\cap B)=0.02\).

Step2: Substitute the values into the formula

Substitute \(P(A\cap B) = 0.02\) and \(P(B)=0.13\) into the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). So \(P(A|B)=\frac{0.02}{0.13}\).

Step3: Calculate the value

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

Step4: Convert to percentage

Multiply the result by 100 to get the percentage. \(0.1538\times100 = 15.38\%\). Rounding to the nearest whole percent gives \(15\%\).

Answer:

\(15\%\)