Example 4.3 On any given day Gary is either cheerful (C), so-so (S), or glum (G). If he is cheerful today, then he will be C, S, or G tomorrow with respective probabilities 0.5, 0.4, 0.1. If he is feeling so-so today, then he will be C, S, or G tomorrow with probabilities 0.3, 0.4, 0.3. If he is glum today, then he will be C, S, or G tomorrow with probabilities 0.2, 0.3, 0.5. Letting X, denote Gary's mood on the nth day, then {Xn, n > 0} is a three-state Markov chain (state 0 = C, state 1 = S, state 2 = G) with transition probability matrix 0.5 0.4 0.1 P = 0.3 0.4 0.3 0.2 0.3 0.5 10. In Example 4.3, Gary is currently in a cheerful mood. What is the probability that he is not in a glum mood on any of the following three days?