Diversion: How Many Sons & Daughters?

Mathematicians (statisticians, more precisely), why isn't the answer 50%?

There's a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What fraction of the population is female?

Don't look for tricks. E.g., assume there's a 50-50 chance for each sex in each birth and that each family can have a limitless number of babies.

For the explaination, see A Big Answer by Steve Landsburg, December 22, 2010 at The Big Questions.