Question: Consider a circular random walk in which six points 1, 2, ... , 6 are placed, in a clockwise order, on a circle. Suppose that one-step transitions are possible only from a point to its adjacent points with equal probabilities. Starting from 1,
(a) find the probability that in 4 transitions the Markov chain returns to 1;
(b) find the probability that in 5 transitions the Markov chain enters to an adjacent point of 1, namely, to 2 or 6.