## Tuesday, 1 February 2011

I'm sure a lot of you are going to be annoyed by this.... but it is just a simple case of where common sense is wrong :)

I have two children, and at least one of them is a son. What is the probability that the other is also a son?

If I have only one child, the probability is $\frac{1}{2}$ that it’s a boy.

But if I have two children, there are really four possibilities, depending on birth order: boy-boy, boy-girl, girl-boy, girl-girl. You know that at least one child is a boy, so you can exclude the girl-girl option. Of the three that remain, only one has two boys. So the probability that my other child is a boy is $\frac{1}{3}$.

Ta-dah!

Franco said...

haha that's classic math :)

AbstractReality said...

Grade school probability.. damn, I miss it.. now it's Calculus :(

Nathaniel said...

oh snap, it was so simple.

Icky Ray said...

does that = 50%? That was my guess.

BMRMike said...

I hate tricky math.

Craig said...

I dispute this - you've counted the boy-girl option twice, albeit born in a different order. The answer should be 50%.

The probability that at least one child is a son, given that you have two children, would be a third.