11. On a given vacation day, a sportsman goes horseback riding (activity 1), sailing (activity 2), or scuba diving (activity 3). Let Xn = 1 if he goes horseback riding on day n, Xn = 2 if he goes sailing on day n, and Xn = 3 if he goes scuba diving on that day.

Suppose that {Xn : n = 1, 2, . . .} is a Markov chain, and depending on which one of these activities the sportsman chooses on a vacation day, his probability of engagement in any one of the activities on the next vacation day is given by the following transition probability matrix:

Find the long-run probability that, on a randomly selected vacation day, the sportsman sails.

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/0.20 0.30 0.50 P=0.32 0.15 0.53 0.60 0.13 0.27,