50% of the country has one male child.
25% of the country has one male and one female child.
12.5% ... 2 females, one male
6.25% ... 3 females, one male
3.125% ... 4 females, one male
etc etc
Or you can look at it this way:
50% of the country has at least 1 girl - contributing P/2 to the girl population
25% of the country has a 2nd girl - contributing P/4 to the girl population
12.5% of the country has a 3rd girl - contributing P/8 to the girl population
...
so the total number of girls is P(1/2+1/4+1/8+ ...) = P.
Or, you can fall back to the axioms: there are n trials, and on average n/2 of them will be girls. The trial conditions are irrelevant to the probability. This is just a bit hard to grok.