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.26%C.51%D.14%SUBMITarrow_backPREVIOUS
Question
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.26%C.51%D.14%SUBMITarrow_backPREVIOUS
Solution
To solve this problem, we need to use the formula for conditional probability, which is P(A|B) = P(A ∩ B) / P(B).
Here, we want to find the probability that a student participates in music lessons given that the student participates in after-school sports. So, event A is "participating in music lessons" and event B is "participating in after-school sports".
From the problem, we know that:
P(B) = 53% = 0.53 (the probability that a student participates in after-school sports)
P(A ∩ B) = 27% = 0.27 (the probability that a student participates in both after-school sports and music lessons)
Substituting these values into the formula, we get:
P(A|B) = P(A ∩ B) / P(B) = 0.27 / 0.53 ≈ 0.5094
So, the probability that a student participates in music lessons given that the student participates in after-school sports is approximately 0.5094, or 51%. Therefore, the correct answer is C. 51%.
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