A particle starts at (4, 4). Each turn, it moves either 1 unit in the −x direction, 1 unit in the −y direction, or 1 unit in each of the −x and −y directions. During a turn, the particle decides how it will move randomly such that the probability of each option is 31. The particle repeatedly takes turns until it hits the x or y axes for the first time. Compute the probability that the particle hits the origin.
