Boys and Girls

Question:

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)

Answer:

“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

Lets consider number of couple are 1000…
at first half couple have boys means half couple have girls..
G=1000/2(Continues…), B=1000/2(Stops…)
at second half couple have boys means half couple have girls..
G=1000/2 + 500/2(Continues…) B=1000/2+500/2(Stops..)
and so on…
at the end ratio of boys to girls is 1:1…