A department store that bills its charge-account cus-tomers once a month has found that if a customer pays promptly one month, the probability is 0.90 that he orshe will also pay promptly the next month; however, if a customer does not pay promptly one month, the prob-ability that he or she will pay promptly the next month is only 0.40. (Assume that the probability of paying or notpaying on any given month depends only on the outcomeof the previous month.)(a) What is the probability that a customer who payspromptly one month will also pay promptly the nextthree months?(b) What is the probability that a customer who does notpay promptly one month will also not pay promptly thenext two months and then make a prompt payment themonth after that?

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Author:Amos Gilat
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A department store that bills its charge-account cus-
tomers once a month has found that if a customer pays
promptly one month, the probability is 0.90 that he or
she will also pay promptly the next month; however, if
a customer does not pay promptly one month, the prob-
ability that he or she will pay promptly the next month is
only 0.40. (Assume that the probability of paying or not
paying on any given month depends only on the outcome
of the previous month.)
(a) What is the probability that a customer who pays
promptly one month will also pay promptly the next
three months?
(b) What is the probability that a customer who does not
pay promptly one month will also not pay promptly the
next two months and then make a prompt payment the
month after that?
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