# C Consumers in Shelbyville have a choice of one of twofast food restaurants, Krustys and

Chapter 3, Problem 49

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C Consumers in Shelbyville have a choice of one of twofast food restaurants, Krustys and McDonalds. Both have troublekeeping customers. Of those who last went to Krustys, 65%will go to McDonalds next time, and of those who last went toMcDonalds, 80% will go to Krustys next time.(a) Find the transition matrix describing this situation.(b) A customer goes out for fast food every Sunday, and just wentto Krustys.i. What is the probability that two Sundays from now she willgo to McDonalds?ii. What is the probability that three Sundays from now she willgo to McDonalds?(c) Suppose a consumer has just moved to Shelbyville, and thereis a 40% chance that he will go to Krustys for his first fast foodouting. What is the probability that his third fast food experiencewill be at Krustys?(d) Find the steady-state vector

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