Question

Your new neighbors have 2 children and you know at least one of them is a boy. You see one of them playing in the backyard and he is a boy - what is the probability the other child is a boy too? (Assume boys and girls are born with equal probability)

Answer 1

It's important to realize that you don't know whether you are looking at the younger or older child. The children could have been born in the following ways: \(B B, B G, G B\). We are excluding the possibility that the children were born \(G G\), since we know that one of the kids is a boy.
\(P(2\) boys \(\mid\) at least 1 boy \()=P(B B) / P(B B \cup B G \cup G B)=1 / 3\)