Detective Plod was putting together the suspect's profile. He had mentioned that he had two children and he had also mentioned that one of them was a boy. What is the probability that his other child is also a boy?

It's not what you may think!

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The obvious answer is one half but consider the following.

If there are two children in a family there are four equally likely possibilities:

The first child is a boy and the second child is also a boy.

The first child is a boy and the second child is a girl.

The first child is a girl and the second child is a boy.

Both children are girls.

As we know one of the children is a boy we are left with three possibilities:

The first child is a boy and the second child is also a boy.

The first child is a boy and the second child is a girl.

The first child is a girl and the second child is a boy.

Of these three possibilities only one of them has the other child a boy. So the answer is one third.

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