Suppose that the weather in a particular region behaves according to a markov chain. specifically, suppose that the probability that tomorrow will be a wet day is 0.666 if today is wet and 0.250 if today is dry. the probability that tomorrow will be a dry day is 0.750 if today is dry and 0.334 if today is wet.

(a) write down the transition matrix for this markov chain. (order the rows and columns by dry first, then wet.) [0.750 0.658 0.250 0.34]
(b) if monday is a dry day, what is the probability that wednesday will be wet?
(c) in the long run, what will the distribution of wet and dry days be?