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?

If the probability that all students participate in after school sports is 53 percent and 27% is the probability that a student will participate in BOTH after school sports and music lessons. The sum of the two probabilities is 80%. The total sum of the percentage probability should always be 100%. Therefore, the probability that a student participates in music lessons is 100 - 80, 20%.

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MrRoyal MrRoyal · Answer 2 · 2022-06-01T09:25:06-04:00

The probability that a student participates in music lessons given that the student participates in after school sports is 50.94%

How to determine the probability?

The given parameters are:

P(After school sport) = 53%
P(After school sport and Music lesson) = 27%

The required probability is calculated using:

P(Music lessons given that after school sports) = P(After school sport and Music lesson)/P(After school sport)

So, we have:

P(Music lessons given that after school sports) = 27%/53%

Evaluate

P(Music lessons given that after school sports) = 50.94%

Hence, the required probability is 50.94%