Question
Rent-A-Jalopy rents cars in NJ, NY, and PA. Some times cars are picked up and returned in the same state. Other times the cars are
Rent-A-Jalopy rents cars in NJ, NY, and PA. Some times cars are picked up and returned in the same state. Other times the cars are picked up in one state and returned in another.
- Of the cars rented in NJ, 50% are returned to NJ, 25% are returned to NY, and 25% are returned to locations in PA.
- Of the cars rented in NY, 20% are returned to NJ, 60% are returned to NY, and 20% are returned to locations in PA.
- Of the cars rented in PA, 10% are returned to NJ, 20% are returned to NY, and 70% are returned to locations in PA.
Use the matrix tool to answer the following questions. (Give your answers correct to 3 decimal places.)
(a) If a car is rented in NJ, what is the probability it will be in NY after it has been rented twice? (b) If a car is rented in NY, what is the probability it will be in PA. after it has been rented three times? (c) In the long run, what fraction of the time does a rental car spend in NJ? In the long run, what fraction of the time does a rental car spend in NY? In the long run, what fraction of the time does a rental car spend in PA?
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