I am ashamed to admit how many hours in the last few days I have devoted to this silly problem I first read on Steve Landsburg’s blog:
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?
Well, of course, you can’t know for sure, because, by some extraordinary coincidence, the last 100,000 families in a row might have gotten boys on the first try. But in expectation, what fraction of the population is female? In other words, if there were many such countries, what fraction would you expect to observe on average?
I have many things to say about it–my brother (who was in a PhD math program) and I argued for a good hour last night alone. But I am way behind on “real work” and so can’t do it justice.
This is not for everyone, but for those who are geeky enough, it’s actually pretty interesting to delve into this controversy. So here’s my plan for you, to get up to speed such that you will fully appreciate my attempt to resolve the dispute when I post it at some unspecified time in the future:
(1) Read Landsburg’s original statement of the problem. Try to figure it out yourself, then skim the comments to see all the knots his readers tied themselves into.
(2) Read Landsburg’s purported solution.
(3) Read the physicist who thinks Landsburg is wrong.
(4) Go back to the comments of Landsburg’s solution post, and skim them. A few people keep hitting on the key elements of the controversy. (To give you a hint: It’s crucial that not every “potential population” has the same size.)
(5) Finally go read Landsburg’s $15,000 challenge to the physicist.