 The solutions in this section consider just those cases in which the player picked door 1 and the host opened door 3.If we assume that the host opens a door at random, when given a choice, then which door the host opens gives us no information at all as to whether or not the car is behind door 1.In the simple solutions, we have already observed that the probability that the car is behind door 1, the door initially chosen by the player, is initially .