A small town has 3 Redbox movie rental boxes. If someone rents a movie at the gr

Question

A small town has 3 Redbox movie rental boxes. If someone rents a movie at the grocery story, there's a 50% chance they'll return it to the grocery story, at 25% chance they'll return it to the drug store, and 25% chance they'll return it to the 7-11 store. If someone rents a movie at the drug store, there as 60% chance they'll return it to the drug store, a 15% chance they'll return it to the grocery store, and a 25% chance it will be returned at 7-11. Of those who rent at 7-11, 55% return it to 7-11, 5% return it to the grocery story, and 40% return it to the drug store. Set up the stochastic matrix for this situations. Put the columns in order: grocery store, drug store, 7-11. If a new movie is put in the grocery store box, what is the probability it will be at the drug store after 3 rental cycles?

Explanation / Answer

1) The setup stochastic matrix will be

0.50 0.15 0.05 0.25 0.60 0.55 0.25 0.25 0.40

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