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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they have a sister?Has a brother Does not have a brotherHas a sister 2 3Does not have a sister 14 7AnswerAttempt 1 out of 5

Question

In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they have a sister?Has a brother Does not have a brotherHas a sister 2 3Does not have a sister 14 7AnswerAttempt 1 out of 5

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Solution

To solve this problem, we need to use the concept of conditional probability. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B).

In this case, we want to find the probability that a student has a brother given that they have a sister. So, A is the event "student has a brother" and B is the event "student has a sister".

From the table, we can see that:

  • The number of students who have a sister is 2 (those who have a brother) + 3 (those who do not have a brother) = 5.
  • The number of students who have both a brother and a sister is 2.

So, we can substitute these values into the formula:

P(A|B) = P(A ∩ B) / P(B) = 2 / 5 = 0.4

Therefore, the probability that a student has a brother given that they have a sister is 0.4 or 40%.

This problem has been solved

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