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 Paid 1 made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 <60 Bad 0.3 0.2 0 s 30 0 0.2 0.2 < 60 0 0.5 0.4 Bad 0 0.2 1 (a) What is the probability of an account eventually being paid off f it is currently overdue at most 30 days? |Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Less than 60 days Probability (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? months (c) If the company has $3000 in bills in the "s 30 days" category and 8000 in bills in the "< 60 days" category, how much can the retailer expect will eventuall paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)
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 Paid 1 made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 <60 Bad 0.3 0.2 0 s 30 0 0.2 0.2 < 60 0 0.5 0.4 Bad 0 0.2 1 (a) What is the probability of an account eventually being paid off f it is currently overdue at most 30 days? |Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Less than 60 days Probability (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? months (c) If the company has $3000 in bills in the "s 30 days" category and 8000 in bills in the "< 60 days" category, how much can the retailer expect will eventuall paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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 Paid
made on an overdue account, its improved status depends on the size of the payment. The matrix on
the right describes the changes in status of accounts.
Paid s30 < 60 Bad
0.3 0.2
<30
0.2
0.2
< 60
0.5
0.4
Bad
0.2
1
...
(a) What is the probability of an account eventually being paid off if it is currently overdue at most 30 days?
Currently overdue
Probability
At most 30 days
What is the probability of an account eventually being paid off if it is currently overdue less than 60 days?
Currently overdue
Probability
Less than 60 days
(b) lf an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad?
months
(c) If the company has $3000 in bills in the "s 30 days" category and $8000 in bills in the "< 60 days" category, how much can the retailer expect will eventually be
paid up and how much will eventually be irretrievable bad debt?
Will eventually be paid up debt
Will eventually be irretrievable bad debt
(Round to the nearest dollar as needed.)
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