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Everyone wants a boy

In a country where everyone wants a boy, each family continues having babies till they have a boy. Once they have a boy, the family stops going for a child. If this continues, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)

SOLUTION : Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method.

Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 +

Summing this infinite GP, Number of girls = C , The proportion of boys to girls is 1 : 1.

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