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You random-walk on five points around a circle, starting at 0, and stop once every point has been visited. What is the probability that you stop at point 2?

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Five points labelled 0 to 4 are equally spaced around a circle. You start at 0 and at each step jump to one of the two neighbouring points with equal chance. The game stops as soon as every point has been visited. What is the probability that the game stops at point 2?

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