3. An apparatus consists of two containers C] and 02, and four balls, in one or the other of the two containers. At regular times the following procedure is carried out: with probability 9 a ball is chosen uniformly at random (from all four balls) and is removed from its container and placed in the other one; with probability 1 l9 things are left as they were. Let X" denote the number of balls in container C1 at time n. (a) Explain why X,1 forms a Markov chain with stationary transition probabilities. [b] Complete the following transition matrix P 16 I9 a: a: :1: Elfal 13 33M a: a: P: 0 W2 a: a: a: a: a: a: 13 9K4 a: a: a: a: 13 (c) Classify the states, taking care to distinguish the cases 9 = 0, O