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### Boys and Girls

In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

### Solution

Pretty simple. Half the couples have boys first, and stop. The rest have a girl. Of those, half have a boy second, and so on.

So suppose there are N couples. There will be N boys. There will be an “infinite” sum of girls equal to N/2 + N/4 + N/8 + … As any college math student knows, this sum adds up to N. Therefore, the proportion of boys to girls will be pretty close to 1:1, with perhaps a few more boys than girls because the sum isn’t actually infinite.

Solved by Paul Brinkley

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