Suppose the family has 3 children of different ages. We assume
that all combinations of boys and girls are equally likely.
(a) Formulate precisely the sample space and probability measure
that describes the genders of the three children in the order in
which they are born.
(b) Suppose we see the parents with two girls. Assuming we have
no other information beyond that at least two of the children are
girls, what is the probability that the child we have not yet seen
is a boy?
(c) Suppose we see the parents with two girls, and the parents
tell us that these are the two youngest children. What is the
probability that the oldest child we have not yet seen is a
boy?