Question: 10. On a given vacation day, Francesco either plays golf (activity 1) or tennis (activity 2). For i = 1, 2, letXn = i, if

10. On a given vacation day, Francesco either plays golf (activity 1) or tennis (activity 2).

For i = 1, 2, letXn = i, if Francesco devotes vacation day n to activity i. Suppose that

{Xn : n = 1, 2, . . .} is a Markov chain, and depending on which of the two activities he chooses on a certain vacation day, the probability of engagement in any one of the activities on the next vacation day is given by the transition probability matrix

0.30 P = 0.58 0.70 0.42

Find the long-run probability that, on a randomly selected vacation day, Francesco plays tennis.

0.30 P = 0.58 0.70 0.42

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