Consider a random walk on the simple graph shown below. At step 0, we start the walk from vertex a1. At step t+1, we will move to a random neighbor of the vertex that we visit at step t. Each neighbor is chosen with equal probability. For example, at step 1, we will visit a random neighbor of vertex a1. Since a1 has 6 neighbors, namely b1,a2,...,a6, each of them will be visited with probability 1/6. (a) (10 points) Define pA(t) to be the probability that at step t, we are visiting one of the vertices a1,...,a6. Find a recurrence equation that pA(t) must satisfy, and give a closed-form expression for pA(t). (b) (10 points) Define pa1(t) to be the probability that at step t, we are visiting the vertex a1. Find a recurrence equation that pa1(t) must satisfy, and give a closed-form expression for pa1(t). You may include pA(t) in the recurrence, and the particular solution will be in the same form as pA(t), but with different coefficients.