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
Source: Bruce Torrence, Randolph-Macon College.