Question

a recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. suppose a pair of jeans is selected at random and it is determined that it has front pockets. what is the probability that a randomly selected pair of jeans with front pockets also has back pockets? 0.52 0.60 0.74 0.81

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( A \) is the event of having back pockets, \( B \) is the event of having front pockets.

Step2: Identify Given Probabilities

We know \( P(A \cap B) = 0.48 \) (probability of having both back and front pockets) and \( P(B) = 0.65 \) (probability of having front pockets).

Step3: Calculate the Conditional Probability

Substitute the values into the formula: \( P(A|B) = \frac{0.48}{0.65} \approx 0.74 \).

Answer:

0.74