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{"ops":[{"insert":"A rural community has two television stations, and on Saturday night the local viewers watch either the \u2018Saturday Movie\u2019 or the \u2018Magic Show\u2019. The following transition matrix contains the probabilities of a viewers watching one of the shows in a week, given that she had watched a particular show the preceding week. \n\nThis week Next week\n Movie Magic\nMovie 0.75 0.25\nMagic 0.45 0.55\n\na) Given that a local viewer watched \u2018Magic Show\u2019 this week, use a decision tree to determine the probability that she will watch \u2018Saturday Movie\u2019 in week 4.\n\n b) Determine the steady state probabilities. \n\nc) If the community contains 1200 television sets, how many will turned to each show in the long run? \n\nd) If a prospective local sponsor wanted to pay for commercial time on one of the shows, which show would more likely be selected? Explain.\n"}]}
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