A department store that bills its charge- account customers 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 probability 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?