2. Vito is lost in a maze. At the center of the maze, there are 3 paths. Path 1 leads out of the maze after a 2 minute walk. Paths 2 and 3 lead back to the center of the maze after 2 and 3 minute walks, respectively. Suppose that each time Vito is at the center of the maze he picks path i with probability i/6. Show that, on average, Vito finds his way out in 15 minutes. Hint: Use "First Step Analysis". That is, use the Law of Total Expectation, with respect to his first choice.

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