On a given vacation day, a sportsman either goes horseback riding (activity 1), or sailing (activity 2), or scuba diving (activity 3). For 1 ≤ i ≤ 3, let X n = i, if the sportsman devotes vacation day...

On a given vacation day, a sportsman either goes horseback riding (activity 1), or sailing (activity 2), or scuba diving (activity 3). For 1 ≤ i ≤ 3, let X_n
= i, if the sportsman devotes vacation day n to activity i. Suppose that {X_n
: n = 1, 2,...}is a Markov chain, and depending on which of these activities the sportsman 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

We know that the sportsman did not go scuba diving on the first day of his vacation. What is the probability that he did not go scuba diving on the second and third vacation days either?