Win Steven Landsburg’s Money. Not!

Last week Steven Landsburg posted the classic puzzle:

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?

Being clever and worldly you may suppose that you know the answer, just as I did. 50%, right?

Every birth has a 50% chance of producing a girl. This remains the case no matter what stopping rule the parents are using. Therefore the expected number of girls is equal to the expected number of boys. So in expectation, half of all children are girls.

Clever! Except Landsburg being even more clever shows that the correct answer is in fact less than 50% (with the exact number depending on how many families there are in the country). 

Clever people don't like to be told they are wrong, however, so even after much explanation (follow Landsburg in the comments to the answer post) there remains disagreement. So Landsburg is offering a big money bet:

I am therefore offering to bet him $15,000 that I’m right (with detailed terms described below). If you agree with Lubos, this is your chance to get in on the action. I will take additional bets up to $5000 per person from all comers until such time as I decide to cut this off.

If you want in, you can read the conditions and bet against Steve here.

N.B.: The correct answer does not rely on selection effects (e.g. some families have a greater propensity to have girls) nor does it involve changing the question to the average fraction of girls in a family.


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