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The Transition Matrix Below Shows the Probabilities That Customer Switch

Question 48

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The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week.                                 Next Week  This Week  Don’s  Limmer’s  Don’s 0.90.1 Limmer’s 0.20.8\begin{array}{l}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Next Week }\\\begin{array} { l c c } \text { This Week } & \text { Don's } & \text { Limmer's } \\\hline \text { Don's } & 0.9 & 0.1 \\\text { Limmer's } & 0.2 & 0.8\end{array}\end{array}
If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's?

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