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At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.20. The probability that a student is a senior and plays a sport is 0.08.What is the probability that a randomly selected student plays a sport, given that the student is a senior?A.0.32B.0.17C.0.08D.0.25

Question

At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.20. The probability that a student is a senior and plays a sport is 0.08.What is the probability that a randomly selected student plays a sport, given that the student is a senior?A.0.32B.0.17C.0.08D.0.25

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Solution

The probability that a randomly selected student plays a sport, given that the student is a senior, is calculated using the formula for conditional probability.

The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B).

In this case, event A is that the student plays a sport and event B is that the student is a senior.

We know that P(A ∩ B) = 0.08 (the probability that a student is a senior and plays a sport) and P(B) = 0.25 (the probability that a student is a senior).

Substituting these values into the formula gives us P(A|B) = 0.08 / 0.25 = 0.32.

So, the probability that a randomly selected student plays a sport, given that the student is a senior, is 0.32.

Therefore, the correct answer is A.0.32.

This problem has been solved

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