Henry, a persistent salesman, calls North's Hardware Store once a week hoping to speak with the store's buying agent, Shirley. If Shirley does not accept Henry's call this week, the probability she will do the same next week is 0.35. On the other hand, if she accepts Henry's call this week, the probability she will not do so next week is 0.20.
a. Construct the transition matrix for this problem.
b. How many times per year can Henry expect to talk to Shirley?
c. What is the probability Shirley will accept Henry's next two calls if she does not accept his call this week?
d. What is the probability of Shirley accepting exactly one of Henry's next two calls if she accepts his call this week?
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