easy | probability |

In a world where everyone wants a girl child, each family continues having babies till they have a girl. What do you think will the boy-to-girl ratio be eventually?

Assuming probability of having a boy or a girl is the same and there is no other gender at the time of birth.

1:1

Suppose there are $N$ couples. First time, $N/2$ girls and $N/2$ boys are born. $N/2$ couples retire, and rest half try for another child.

Next time, $N/4$ couples give birth to $N/4$ girls and $N/4$ boys. Thus, even in the second iteration, the ratio is $1:1$. It can now be seen that this ratio will always remain the same, no matter how many times people try to give birth to a favored gender.