Monsieur Bertrand

Abstract

We expect to receive two Olympic medals, and we know that neither of them is bronze. There are three boxes in front of us, each containing two medals. One contains two gold medals (GG), another two silver medals (SS), and the third one gold and one silver medal (GS). The boxes are indistinguishable from one another, each with two drawers containing one medal. This is all the information we know. We select a box at random, open one of the drawers and find a silver medal inside. What is the probability that there will be a gold medal in the other drawer of this box? That seems easy. We have eliminated the possibility of the box containing two gold medals (GG), so there are two hypotheses: we selected the box with two silver medals (SS) or the box with one gold and one silver medal (GS). That seems to be it – the probability of finding gold in the other drawer of the box is 1 in 2.