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.
You meet a stranger on the street, and ask how many children he has. He
truthfully says two. You ask "Is the older one a girl?" He truthfully
says yes. What is the probability that both children are girls? What
would the probability be if your second question had been "Is at least
one of them a girl?", with the other conditions unchanged?
There are four possibilities:
Oldest child Youngest child 1. Girl Girl 2. Girl Boy 3. Boy Girl 4. Boy Boy