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 Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). Here, let \( A \) be the event that a car is an SUV and \( B \) be the event that a car is white. So we need to find \( P(\text{SUV} | \text{white}) \).

Step2: Identify Given Probabilities

We know that \( P(\text{SUV} \cap \text{white}) = 2\% = 0.02 \) (probability a car is a white SUV) and \( P(\text{white}) = 13\% = 0.13 \) (probability a car is white).

Step3: Apply the Formula

Substitute the values into the formula: \( P(\text{SUV} | \text{white}) = \frac{0.02}{0.13} \approx 0.1538 \). Convert this to a percentage: \( 0.1538 \times 100 \approx 15\% \).

Answer:

15% (corresponding to the option "15%")