At the beginning of each year, my car is in good, fair, or broken-down condition

Question

At the beginning of each year, my car is in good, fair, or broken-down condition. A good car will be good at the beginning of next year with probability .85; fair with probability .10; or broken-down with probability .05. A fair car will be fair at the beginning of the next year with probability .70; or broken-down .30. It costs $6000 to purchase a good car; a fair car can be traded in for $2000; and a broken-down car has no trade-in-value and must immediately be replaced by a good car. It costs $1000 per year to operate a good car and $1,500 to operate a fair car.

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