Drunk man on a bridge

A man stands at the 17-meter mark of a 100-meter bridge and takes ±1\pm 1 m steps with equal probability, stopping when he reaches either end (0 m or 100 m). What is the expected number of steps until he reaches an end?

Show hints (2)+
  1. Distances to the two ends are 17 and 83.
  2. E[steps]=αβE[\text{steps}] = \alpha\beta for the symmetric walk.

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1411

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