The People In Puzzletown

Time for a new problem. This one is not very difficult, you should be able to solve it in a matter of minutes, but it has a pretty neat follow-up, so I want to post it. I first learned this on the forums at xkcd.
The parents in puzzletown all want to have boys. Each family will have children until they have had at least one male child, then they will stop having children. On a given birth, it is equally likely that the child will be a boy or a girl. Assuming a large number of families, what is the ratio of boys to girls among the children in puzzletown?

3 comments:

McAnerbot said...

I reduced it to an infinite sum that I do not know how to do, but I may of gone down the wrong path and missed something obvious.

*SPOILER*

1: sum(n=1 -> infinity) (n-1)/2^n

McAnerbot said...

Of course I could just be too lazy to actually look at the sum. And you know engage the ol' brain at 9:45 am.

So yah, got it :)

Lionel Brits said...

I want to say that there are just as many boys as girls, for obvious reasons, but Chewbacca lives on Endor, and so my argument would be invalid.