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 40% chance they'll return it to the grocery story: at 20% chance they'll return it to the drug store, and 40% chance they'll return it to the 7-11 store. If someone rents a movie at the drug store, there as 50% chance they'll return it to the drug store, a 20% chance they'll return it to the grocery store, and a 30% chance it will be returned at 7-11. Of those who rent at 7-11, 75% return it to 7-11, 10% return it to the grocery story, and 15% 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

We set up states as follows

grocery store : 1

Drug store : 2

7-1 store : 3

Now answer is as follows

0.40 0.20 0.40 0.20 0.50 0.30 0.10 0.15 0.75

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