Each week, Ms. Turnham buys one of four kinds of cereal, A, B, C, or D....

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Each week, Ms. Turnham buys one of four kinds of cereal, A, B, C, or D. On the week of January 1st she buys one of these four kinds chosen at random. If she buys A one week, then the probabilities that she will buy A, B, C, or D the next week are 0.4, 0.2, 0.2, and 0.2, respectively. If she buys B one week, then the probabilities that she will buy A, B, C, or D the next week are 0.4, 0.1, 0.2, and 0.3, respectively. If she buys C one week, then the probabilities that she will buy A, B, C, or D the next week are 0.1, 0.1, 0.1, and 0.7, respectively. If she buys D one week, then the probabilities that she will buy A, B, C, or D the next week are 0.3, 0.3, 0.3, and 0.1, respectively. Assuming these transition probabilities do not change over time, what is the probability that Ms. Turnham will buy cereal B on the week of January 14? Each week, Ms. Turnham buys one of four kinds of cereal, A, B, C, or D. On the week of January 1st she buys one of these four kinds chosen at random. If she buys A one week, then the probabilities that she will buy A, B, C, or D the next week are 0.4, 0.2, 0.2, and 0.2, respectively. If she buys B one week, then the probabilities that she will buy A, B, C, or D the next week are 0.4, 0.1, 0.2, and 0.3, respectively. If she buys C one week, then the probabilities that she will buy A, B, C, or D the next week are 0.1, 0.1, 0.1, and 0.7, respectively. If she buys D one week, then the probabilities that she will buy A, B, C, or D the next week are 0.3, 0.3, 0.3, and 0.1, respectively. Assuming these transition probabilities do not change over time, what is the probability that Ms. Turnham will buy cereal B on the week of January 14?

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Lets break this down into a probability tree Week 1 Jan 1 Prob of buying A 14 Prob of buying B 14 Pr... View the full answer