Probablility of Second Child Puzzle

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James and Catherine are a married couple. They have two children, one of the child is a boy. Assume that the probability of each gender is 1/2.

What is the probability that the other child is also a boy?

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Eventhough the individual probability of each gender is 1/2, We have to consider the conditional probability in this problem.

There are only four possible combinations of two children in a family:

Boy Girl

Girl Boy

Boy Boy

Girl Girl

Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.

This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3

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