Problem of the Week 1201

What Goes Up Might Not Come Down

A random walk on the 2-dimensional integer lattice begins at the origin. At each step, the walker moves one unit either left, right, or up, each with probability 1/3. (No downward steps ever.)

A walk is a success if it reaches the point (1, 1).

What is the probability of success?

Note: One can vary the problem by varying the target point. For example, use (1, 0) or (0, 1) instead. Perhaps there is a good method to resolve the general case of target (a, b).

Source: Bruce Torrence, Randolph-Macon College.

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