Fifty two percent of students at a local college works (for pay) in addition to being students, and \( 39 \% \) of the students at the school are parents. \( 14 \% \) of students fit into both categories. At an event specifically for students who are also parents, one randomly selected student parent if asked whether she works a paid job in addition to being a student. What is the probability that this parent works for pay? \( 35.9 \% \) \( 26.9 \% \) \( 56.0 \% \)

To find the probability that a randomly selected student parent works for pay, we can use the concept of conditional probability. Let \( A \) be the event that a student works for pay, and \( B \) be the event that a student is a parent. We need to find \( P(A | B) \), the probability that a student works given that they are a parent. From the problem, we know: - \( P(A) = 0.52 \) (the probability that a student works) - \( P(B) = 0.39 \) (the probability that a student is a parent) - \( P(A \cap B) = 0.14 \) (the probability that a student is both a parent and works) Using the formula for conditional probability: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \] Substituting the known values: \[ P(A | B) = \frac{0.14}{0.39} \approx 0.3589 \] So, converting this to a percentage, we multiply by 100: \[ P(A | B) \approx 35.89\% \] Thus the closest option provided is \( 35.9\% \).