There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes.
However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability of 13 boys in a family with 13 children is approx 0.00019.
1/32
It depends on the context: if you select a child at random from a girls' school, the probability is 0, while if it is at a boys' school it is 1!
50/50
3/8
Assuming that having boys and girls are equally likely, then the probability is 1/8. * * * * * You also need to assume that the children's genders are independent. They are NOT and depend on the parents' ages and genes.