Suppose that three boys A, B, and C are throwing a ball from one 10 another. Whenever A has the ball he throws it to B with a probability of 0.2 and to C with a probability of 0.8. Whenever B has the ball he throws it to A with a probability of 0.6 and to C with a probability of 0.4. Whenever C has the ball he is equally likely to throw it to either A or B.
(a) Consider this process to be a Markov chain and construct the transition matrix.
(b) If each of the three boys is equally likely 10 have the ball at a certain time n, which boy is most likely 10 have the ball at time n + 2?