A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.
(a) Set up the 3 × 3 stochastic matrix that describes this situation.
(b) Suppose that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie. What percent of the students will order cake tomorrow? The day after tomorrow?