A housewife buys three kinds of cereals C1, C2 and C3. It is known that she never buys the same cereal on successive weeks. If she buys cereal C1, then the next week she buys cereal C2. However, if she buys C2 or C3, then the next week she is thrice as likely to buy C1 as the other brand.

Obtain the transition probability matrix and determine how often she would buy each of the cereals in the long run.

The given information is presented in Table 14.3 in the form of a transition probability matrix.

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TABLE 14.3 Transition Probabilities Matrix State State C C C3 555 0 1 0 0.75 0 0.25 0.75 0.25 0