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 do not have a sister?Has a brother Does not have a brotherHas a sister 2 10Does not have a sister 9 6
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 do not have a sister?Has a brother Does not have a brotherHas a sister 2 10Does not have a sister 9 6
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, event A is "having a brother" and event B is "not having a sister".
From the table, we can see that:
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The total number of students is 2 (has a brother and a sister) + 10 (does not have a brother but has a sister) + 9 (has a brother but does not have a sister) + 6 (does not have a brother or a sister) = 27 students.
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The number of students who have a brother and do not have a sister (A ∩ B) is 9.
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The number of students who do not have a sister (B) is 9 (has a brother but does not have a sister) + 6 (does not have a brother or a sister) = 15.
So, the probability that a student has a brother given that they do not have a sister is P(A|B) = P(A ∩ B) / P(B) = 9 / 15 = 0.6 or 60%.
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