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Consider a company that rents electric scooters. At the end of each day, scooter can be either classified in good, fair or poor condition,

 

Consider a company that rents electric scooters. At the end of each day, scooter can be either classified in good, fair or poor condition, as well as broken down. Previous data shows that probability that a scooter breaks down depends on its condition and these probabilities are 0.02, 0.05 and 0.20 for scooters in good, fair and poor conditions, respectively. Moreover, a scooter in good condition degrades to fair condition with probability 0.12 and to poor condition with probability 0.06, while a scooter in fair condition degrades to poor condition with probability 0.15. A broken down scooter must be replaced at a cost of $500 (this occurs immediately). What is the expected daily cost of maintaining a fleet of 5000 scooters? (Hint: keep in mind that a scooter can stay in the same condition it was on the previous day)

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