Solution to warm-up:
Let us represent boys by 1's and girls by 0's. There are eight equally likely scenarios for three children:
In only one case will there be no boys (000). That will happen to only one family in eight. So, 7/8 of the families will have a boy.
One might wonder whether it is legitimate to count as different families with the same set of real children but different sets of phantom children. For example, 100, 101, 110 and 111 all end up as a family with one boy. The best way to think about this is to imagine that the phantom children are in fact real but are sent abroad to a less sexist culture. In that case, every family has three children, but the family possibilities that remain in Machudo are just boy; girl, boy; girl, girl, boy; and girl, girl, girl.