A retailer classifies accounts as having one of four possible states: "paid up," "overdue at most 30 days," "overdue less than 60 days but more than 30 days," and "bad." If no payment is made on an overdue account by the end of the month, the status moves to the next state. When a partial payment is made on an overdue account, its improved status depends on the size of the payment. Experience shows that the following matrix describes the changes in status of accounts:

(a) What is the probability of an account eventually being paid off if it is currently overdue at most 30 days? Less than 60 days?
(b) If an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad?
(c) If the company has $2000 in bills in the "... 30 day" category and $5000 in bills in the "6 60 day" category, how much can the retailer expect will eventually be paid up and how much will eventually be irretrievable bad debt?

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< 60 Bad Paid s 30 Paid 1 4 .1 < 30 4 .4 < 60 .4 Bad .1