Let's
say a mathematician and father of two tells you one of his children is
a boy, then asks what the odds are that the other child is also a boy.
It may seem obvious that the odds are 1 in 2, since the chances of any
given child being born male are the same as a coin toss. But the correct
answer is 1 in 3. Why? The reason is that the father is effectively asking
what the odds are of both children being male, and we already know that
(at least) one of them is. This actually creates three possible scenarios:
two boys, a younger boy and an older girl, or a younger girl and an older
boy. Both children are male in only one of these three scenarios, so the
odds are 1 in 3. If the father had instead told you that, say, the older
child was a boy, then the odds would indeed be 1 in 2 because in this case
there are just two possibilities: The children are either both boys or
a younger girl and an older boy—and two boys are just as likely as one
child of each sex.