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Find the expected number of steps made by a drunk who leaves a bar at position 1 and takes independent steps: left (L) with probability

Find the expected number of steps made by a drunk who leaves a bar at position 1 and takes independent steps: left (L) with probability 2/3 or right (R) with probability 1/3. The drunk stops if he reaches home (at position 0) or the lockup (at position 3)

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