The following question is taken from the book titled "Probability models for Computer Science" written by Sheldon M. Ross.
A particle moves along n + 1 vertices that are situated on a circle in the following manner. At each stage the particle moves one step that is either in the clockwise direction with probability p or in the counter-clockwise direction with probabiity 1-p.
Starting at a specified state let T denote the time of the first return to that state. Now how to find the probability that the particle has visited all the vertices by time T