Random Steps of a Drunk Man: Probability of Escaping the Cliff

Problem
From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?

A.   2/27 C.   4/27
B.   107/243 D.   1/2

 

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