Question: A kindergartner is going through that phase when she only eats certain foods. For breakfast she only eats Lucky CharmsTM, Cap'n CrunchTM, or Froot LoopsTM.

A kindergartner is going through that phase when she only eats certain foods. For breakfast she only eats Lucky CharmsTM, Cap'n CrunchTM, or Froot LoopsTM. Her parent notices that if she eats one cereal on a given day, on the next day she will eat the same cereal with probability of 50%, and she will choose one of the other cereals with probability of 25%.

(a) What is the stochastic matrix for this situation?

(b) If she chooses Cap'n CrunchTM on Monday, what is the probability she will choose Froot LoopsTM on Wednesday?

(c) If she chooses Lucky CharmsTM on Sunday and Cap'n CrunchTM on Monday, what is the probability she will choose Froot LoopsTM on Wednesday?

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