Puzzle #9: Boys and Girls | Amazon

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)

Puzzle Solution:

“Very 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.

1/2 have a boy and stop: 0 girls

1/4 have a girl, then a boy: N/4 girls

1/8 have 2 girls, then a boy: 2*N/8 girls

1/16 have 3 girls, then a boy: 3*N/16 girls

1/32 have 4 girls, then a boy: 4*N/32 girls

…

Total: N boys and

1N 2N 3N 4N

– + – + – + — +… = ~N

Therefore, the proportion of boys to girls will be pretty close to 1 : 1

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