Question: the following variant of the Let's Make a Deal game. Again one of the three boxes contains a prize, but now there are two players, 1 and 2. Assume Player 1 picks Box A and Player 2 picks Box B. The host (who again has perfect knowledge) opens Box B, which contains junk, and Player 2 leaves the show. Player 1 can either stay with Box A or switch to Box C. Using Bayes' theorem, show that now it does not pay Player 1 to switch, that is, the probability Player 1 will win with Box C is 1/2, the same as the probability Player 1 will win by staying with Box A.