Fuzzy Math: Reproductive Roulette

If a father of two tells you one of his children is a boy, what are the odds that the other child is also a boy?

By Alex Stone|Tuesday, August 01, 2006
RELATED TAGS: MATH

Let's say a mathematician and father of two tells you one of his children is a boy, then asks what the odds are that the other child is also a boy. It may seem obvious that the odds are 1 in 2, since the chances of any given child being born male are the same as a coin toss. But the correct answer is 1 in 3. Why?

The reason is that the father is effectively asking what the odds are of both children being male, and we already know that (at least) one of them is. This actually creates three possible scenarios: two boys, a younger boy and an older girl, or a younger girl and an older boy. Both children are male in only one of these three scenarios, so the odds are 1 in 3.

If the father had instead told you that, say, the older child was a boy, then the odds would indeed be 1 in 2 because in this case there are just two possibilities: The children are either both boys or a younger girl and an older boy—and two boys are just as likely as one child of each sex.

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