Suppose that three boys A, B, and C are throwing a ball from one to 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 to have the ball at a certain time n, which boy is most likely to have the ball at time n + 2?