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!
6 comments:
haha that's classic math :)
Grade school probability.. damn, I miss it.. now it's Calculus :(
oh snap, it was so simple.
does that = 50%? That was my guess.
I hate tricky math.
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.
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