This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
If a person has two children, and truthfully answers yes to the question
"Is at least one of your children a girl?", what is the probability that
both children are girls?
The answer is 1/3, assuming that it is equally likely that a child will be
a boy or a girl. Assume that the children are named Pat and Chris: the
three cases are that Pat is a girl and Chris is a boy, Chris is a girl and
Pat is a boy, or both are girls. Since one of those three equally likely
possibilities have two girls, the probability is 1/3.