There is a country where everyone wants a boy. Every family continue to have babies till a boy is born. If the probability of having a girl or a boy is the same, what is the proportion of boys to girls after some time in that country?

Since the probability of having a girl or a boy is same, half of the families will have a boy first and stop. The other half of the families will have a girl and from half of those families, the second born will be a boy and they will stop while the others will again have a girl. This process will continue.

Suppose the number of couples are N, the number of boys will be N.

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 girl will be quite close to 1:1.