Question

question 19 of 39
at taft high school, 59% of all students participate in after - school sports and 23% participate in both after - school sports and volunteer activities. what is the probability that a student participates in volunteer activities given that the student participates in after - school sports?
a. 82%
b. 39%
c. 36%
d. 59%

Explanation:

Step1: Use conditional probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event of participating in volunteer activities and \(B\) be the event of participating in after - school sports. We are given \(P(B) = 0.59\) (59%) and \(P(A\cap B)=0.23\) (23%).

Step2: Calculate the probability

Substitute the values into the formula: \(P(A|B)=\frac{0.23}{0.59}\approx 0.39\) (or 39%).

Answer:

B. 39%