The Matrix of Transition Probabilities Below Deals with Brand Loyalty

The matrix of transition probabilities below deals with brand loyalty to Bark Bits and Canine Chow dog food. $$\begin{array} { c | c c } \text { Current } & { \text { Next Purchase } } \\\text { Purchase } & \text { Bark Bits } & \text { Canine Chow } \\\hline \text { Bark Bits } & .75 & .25 \\\text { Canine Chow } & .20 & .80\end{array}$$
a.What are the steady state probabilities?
b.What is the probability that a customer will switch brands on the next purchase after a large number of periods?

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