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Boys and Girls

Ratio of Boys and Girls

Ques:

In a country where everyone wants a boy, each family continues having babies until they have a boy. After some time, the proportion of boys to girls in the country is X: 1.

What is the value of X?

Solution :
Number of girls = 0*(Probability of 0 girl) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + …
Number of girls = 0*(X*1/2) + 1*(X*1/2*1/2) + 2*(X*1/2*1/2*1/2) + …
Number of girls = 0 + X/4 + 2*X/8 + 3*X/16 + …
Number of girls = X
(Assume that the probability of having a boy or a girl is the same.)
The proportion of boys to girls is 1: 1.