Futility Closet

“Boy Trouble”: Solution

Posted in Puzzles, Science & Math by Greg Ross on September 6th, 2007

Solution to Boy Trouble:

If I have only one child, the probability is 1/2 that it’s a boy.

But if I have two children, there are really four possibilities, depending on birth order: boy-boy, boy-girl, girl-boy, girl-girl. You know that at least one child is a boy, so you can exclude the girl-girl option. Of the three that remain, only one has two boys. So the probability that my other child is a boy is 1/3.