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At Franklin High School, 15% of the students play basketball and 4% of the students play baseball and basketball. What is the probability that a student plays baseball given that he or she plays basketball?A.37.5%B.26.7%C.6%D.0.6%

Question

At Franklin High School, 15% of the students play basketball and 4% of the students play baseball and basketball. What is the probability that a student plays baseball given that he or she plays basketball?A.37.5%B.26.7%C.6%D.0.6%

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Solution

The question is asking for the probability that a student plays baseball given that he or she plays basketball. This is a conditional probability problem.

Here are the steps to solve it:

  1. Identify the given probabilities:

    • The probability that a student plays basketball, P(Basketball) = 15% or 0.15
    • The probability that a student plays both baseball and basketball, P(Baseball ∩ Basketball) = 4% or 0.04

  2. Use the formula for conditional probability, which is P(A|B) = P(A ∩ B) / P(B). In this case, we want to find P(Baseball|Basketball) = P(Baseball ∩ Basketball) / P(Basketball).

  3. Substitute the given probabilities into the formula: P(Baseball|Basketball) = 0.04 / 0.15

  4. Calculate the result: P(Baseball|Basketball) = 0.2667 or 26.67%

So, the probability that a student plays baseball given that he or she plays basketball is approximately 26.67%, which corresponds to option B.

This problem has been solved

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