91Ó°ÊÓ

A survey of American car buyers indicates that if a person buys a Ford, there is a \(60 \%\) chance that their next purchase will be a Ford, while owners of a GM will buy a GM again with a probability of .80 . The buying habits of these consumers are represented in the transition matrix below. Find the following probabilities: a. The probability that a present owner of a Ford will buy a \(\mathrm{GM}\) as his next car. b. The probability that a present owner of a GM will buy a GM as his next car. c. The probability that a present owner of a Ford will buy a \(\mathrm{GM}\) as his third car. \left.\begin{array}{c} \text { Next Purchase } \\ \text { Ford } & \text { GM } \\ \text { .60 } & .40 \\ .20 & .80 \end{array}\right]

Professor Hay has breakfast at Hogee's every morning. He either orders an Egg Scramble, or a Tofu Scramble. He never or ders Eggs on two consecutive days, but if he does order Tofu one day, then the next day he can order Tofu or Eggs with equal probability. a. Write a transition matrix for this problem. b. If Professor Hay has Tofu on the first day, what is the probability he will have Tofu on the second day? c. If Professor Hay has Eggs on the first day, what is the probability he will have Tofu on the third day? d. If Professor Hay has Eggs on the first day, what is the probability he will have Tofu on the fourth day?