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?
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.
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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
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 :)
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.
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