An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found that from May through September, when it rains one day, the probability of rain for the next day is 0.5; when it does not rain one day, the probability of rain for the next day is 0.08.

A) Draw a transition diagram representing the transition between the states "Open" and "Closed"
B) Give the transition probability matrix P
C) Suppose that on Tuesday, May 1t it rains. Use this fact to give the initial state distribution matrix So
D) Knowing that it rained on Tuesday, what is the probability that the restaurant will be closed on Thursday, the first day of your vacation?