  Initially proposed by Martin Gardner in the 1950s, the famous two-children
problem is often presented as a paradox in probability theory. A relatively
recent variant of this paradox states that, while in a two-children family for
which at least one child is a girl, the probability that the other child is a
boy is $2/3$, this probability becomes $1/2$ if the first name of the girl is
disclosed (provided that two sisters may not be given the same first name). We
revisit this variant of the problem and show that, if one adopts a natural
model for the way first names are given to girls, then the probability that the
other child is a boy may take any value in $(0,2/3)$. By exploiting the concept
of Schur-concavity, we study how this probability depends on model parameters.
