The issue with asking whether the other is a girl is how you choose the first one. If you look at one random child, see it's a boy and exclude the family, even

The issue with asking whether the other is a girl is how you choose the first one. If you look at one random child, see it's a boy and exclude the family, even though the other child may be a girl, then you get the 1/2 probability. If however in that case you also look at the second child, see that's a girl and consider the family anyway, then you get the 1/3