In one nation, having a daughter is traditionally prefferable to having a son. Therefore, a couple will continue to have children until a daughter is born. Once they have a daughter, they will stop. (Assume that it is possible for a couple to have an unlimited number of children)

If the chance of a boy or a girl being born is equal, what would be the ratio boys to girls in this country?

(In reply to re: Wasn't it obvious? by levik)

In "real life" the odds, while not exactltly 50:50 are close enough to it for the general population. For individual attempts at conception, there are many factors that can greatly affect those odds, and many of those factors turn affect China's statistics.

But in the land of the puzzle, the odds, both in the total population and in the individual case, are stated to be exactly 50:50.

Yes, one of the easiest ways to prove it requires the infinte series 1 = 1/2 + 1/4 + 1/8 + ...,

but there is the following argument which does not involve infinities, and which shows the individual practice does not affect the outcome:

Assume that this year there are P1 women pregnant for the first time in the hospital, P2 women pregnant for the second time, etc. for a total of P' pregnant women. There will be P'/ boys born and P'/2 girls (Since in this ideal world hemaphrodites presumably do not exist, in years when P' is odd, there is one extra boy or one extra girl, but even that evens out over a large enough number of years. Even assuming that the pre-existing child population was wildly uneven the first year, after a sufficient (and relatively small) number of years, their numbers will have fallen off, (through death and growth to adulthood) and only thosee born during the "watched" year will remain. Their proportion, by age is always 1:1, and so their proportion as a group is also 1:1.

Posted by TomM on 2002-07-08 22:01:20