Sex ratio when families stop at a daughter

In a remote community every couple keeps having children until their first daughter is born, then stops. Boys and girls are equally likely at each birth, independently. In the long run, what fraction of the population is female?

$1/2$. Every birth is still an independent fair coin, and a stopping rule cannot change the expected proportion of girls among births. Concretely, each couple has exactly one girl and on average $2$ children, so half of all children are girls.