If a woman's first two children are girls, what are the odds that her third child will be a girl?

This is a classic statistics question to which most of you will know the answer. The answer, of course is about 50:50 (i.e. 0.5).

Intuitively, we may feel that the odds of such a thing happening three times in a row is improbable. And it is. The odds of having three girls in a row is about 1:8 (i.e. 0.5³).

But that is not what the question is asking. We already know that the first two children are girls, and thus this history is an irrelevant red herring. There's no difference between asking the question in the heading above and asking what the odds of having a girl for your first (or second, or seventh) child are.

Of course, as super-educated geniuses we doctors can chuckle at anyone who makes such a "schoolboy error". But you'd be surprised how hard it can be to explain this sort of basic statistical concept to a patient sometimes. ("You have a 1-in-4 chance of your offspring developing your genetic condition. But that doesn't mean that if the first child is affected, the next three will be OK.")