Now consider the Monty Hall dilemma from Section 6.1 with the following difference: you learned beforehand that there is a 0.2 probability of the automobile being behind door 1, a 0.3 probability of its being behind door 2, and a 0.5 probability of its being behind door 3. Your strategy is to choose the door with the lowest probability (door 1) in the first round of the game, and then to switch doors to one with a higher probability after the host has opened a gag prize door. Set up a chance tree to determine your probability of winning the automobile.

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