Question

question 11 of 40
at howard high school, 53% of all students participate in after - school sports and 27% participate in both after - school sports and music lessons. what is the probability that a student participates in music lessons given that the student participates in after - school sports?

a. 80%

b. 14%

c. 26%

d. 51%

Explanation:

Answer:

D. 51%

To find the conditional probability \( P(\text{music} | \text{sports}) \), we use the formula for conditional probability: \( P(A | B) = \frac{P(A \cap B)}{P(B)} \). Let \( A \) be "participates in music lessons" and \( B \) be "participates in after - school sports". We know that \( P(B)=0.53 \) (or 53%) and \( P(A\cap B) = 0.27 \) (or 27%). Then \( P(\text{music} | \text{sports})=\frac{0.27}{0.53}\approx0.51 = 51\% \).