Coffeehouse Post

• Dr Herbie said:
It's 50%.

The sex of the second child is not affected at all by the sex of the first child; knowing that one of the children is a girl is irrelevant in detemining the sex of the other.

Trust me, I'm a Doctor (of biology)

Herbie
It depends on how you interpret the question.

If you interpret the question as: my first child is a girl. Now my wife is pregnant, what are the odds of the other one being a boy? Then it's 50%.

However, if you interpret it as: we already have two children, one of whom is a girl. How likely is it that the other is a boy? Then we must consider the following: the likelyhood of having two boys is 50% * 50% = 25%. The likelyhood of having two girls is also 50% * 50% = 25%. The likelyhood of having a boy and a girl is 50% * 50% + 50% * 50% = 50%.
With the added information that one child is a girl, we know that two boys are impossible. We are therefore left with either boy and girl at 66% or two girls at 33%. So in 66% of the remaining scenarios, the second child is a boy.

The disagreement people are having is one of semantics, not maths.