Assume the country has **N** families. Since every family will have children until a daughter is born, they will have **N** daughters.
But there is a 1/2 chance that the first child will be a boy, making for **N/2** "firstborn" boys.
There is also a 1/4 chance that the second child will be a boy as well, for a total of **N/2 + N/4** boys among the first- and second-born.
It is easy to see that after each child, the chance that all the children are boys is reduced by 1/2, so the total number of boys is equal to **N/2 + N/4 + N/8 + ...**, an infinite series that adds up to **N**.
So the ratio of boys/girls in the country will actually be 1 to 1, unaffected by the strange custom. |