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 \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( P(A|B) \) is the probability of event \( A \) given event \( B \), \( P(A \cap B) \) is the probability of both \( A \) and \( B \) occurring, and \( P(B) \) is the probability of event \( B \).

Step2: Identify Events and Probabilities

Let \( A \) be the event that a car is an SUV, and \( B \) be the event that a car is white. We know:

• \( P(A \cap B) = 2\% = 0.02 \) (probability of white SUVs)
• \( P(B) = 13\% = 0.13 \) (probability of white cars)

Step3: Apply the Formula

Substitute the values into the formula: \( P(A|B) = \frac{0.02}{0.13} \approx 0.1538 \), which is approximately \( 15\% \) when rounded to the nearest whole percent.

Answer:

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