Question

In a class of 27 students, 10 have a brother and 12 have a sister. There are 7 students who do not have any siblings. What is the probability that a student who has a sister also has a brother?

Answer 1

1/6

Explanation:

You want the probability that a student with a sister also has a brother, given that of 27 students, 10 have a brother, 12 have a sister, and 7 have no siblings.

Both

The number of students with a brother or sister is 27 -7 = 20. The number that have both a brother and sister is then ...

P(B or S) = P(B) +P(S) -P(B&S)

P(B&S) = P(B) +P(S) -P(B or S) = (10 +12 -20)/27 = 2/27

Conditional

The conditional probability that a student with a sister also has a brother is ...

P(B | S) = P(B&S) / P(S) = (2/27)/(12/27) = 2/12 = 1/6

The probability that a student with a sister also has a brother is 1/6.

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