Bertrand’s box paradox a puzzle concerning conditional probability. Imagine three boxes with two drawers apiece. Each drawer of the first box contains a gold medal. Each drawer of the second contains a silver medal. One drawer of the third contains a gold medal, and the other a silver medal. At random, a box is selected and one of its drawers is opened. If a gold medal appears, what is the probability that the third box was selected? The probability seems to be ½, because the box is either the first or the third, and they seem equally probable. But a gold medal is less probable from the third box than from the first, so the third box is actually less probable than the first. By Bayes’s theorem its probability is 1/3. Joseph Bertrand, a French mathematician, published the paradox in Calcul des probabilités (Calculus of Probabilities, 1889). See also BAYES’s THEOREM , PROBABILIT. P.We.