A shopping mall is considering adopting a new credit management policy in an attempt to

reduce the number of credit customers defaulting on their payments. The credit manager

has suggested that in the future credit should be discounted to any customer who has

twice been a week or more late with his monthly instalment payment. She supports her

claim by noting that past credit records show that $90\%$ of all those defaulting on their

payments were late with at least two monthly instalments.

Suppose from investigations it has been found that $2\%$ of all credit customers actually

default on their payments and that $45\%$ of those who have not defaulted have had at least

two late monthly payments.

$($i$)$ Using Bayes$$ analysis, determine the probability that a customer with two or more

late payments will actually default on his payments $(5$ Marks$)$

$($ii$)$ In light of the probability value obtained in $($i$)$ above, criticize the credit manager$$s

credit plan