# There are three types of grocery stores in a given community. Within this community (with a fixed po

There are three types of grocery stores in a given community. Within this community (with a fixed population) there always exists a shift of customers from one grocery store to another. On January 1, (1/4) shopped at store I (1/3) at store II and (5/12) at store III. Each month store I retains 90% of its customers and loses 10% of them to store II. Store II retains 5% of its customers and loses 85% of them to store I and 10% of them to store III. Store III retains 40% of its customers and loses 50% of them to store I and 10% to store II. a) Find the transition matrix. b) What proportion of customers will each store retain by Feb. 1 and Mar. 1?

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