Thread: probability word problem involving percents and banking

A bank is reviewing its credit policy with a view toward recalling some of its credit cards. It has been found 5% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. The bank has also found that the probability of missing one or more payments is 0.2 for customers who do not dfault. The probability for customers who default is, of course, 1. Should the bank recall its card if the probability that a customer will defualt is greater than 0.2? Why?

The first step is to determine the probability that a customer will defualt. I tried drawing a tree diagram but I'm not sure what goes on the first level. Defaulting depends on missed payments, right? But wouldn't that mean that there's a 5% chance for anyone to default, reguardless of their missed payments?

Originally Posted by Jskid

A bank is reviewing its credit policy with a view toward recalling some of its credit cards. It has been found 5% of cardholders have defaulted and the bank has been unable to collect the outstanding balance. The bank has also found that the probability of missing one or more payments is 0.2 for customers who do not dfault. The probability for customers who default is, of course, 1. Should the bank recall its card if the probability that a customer will defualt is greater than 0.2? Why?

The first step is to determine the probability that a customer will defualt. I tried drawing a tree diagram but I'm not sure what goes on the first level. Defaulting depends on missed payments, right? But wouldn't that mean that there's a 5% chance for anyone to default, reguardless of their missed payments?

I don't understand "Should the bank recall its card if the probability that a customer will defualt is greater than 0.2? Why?" Is there more to the question that you haven't posted eg. Does the bank want the probability of missed payments to be below a certain threshold?

As for the tree diagram, one possibility is to have the first level of branches being D (Default) and D' and the secnd level of branches being M (Missed one or more re-payments) and M'.

The question verbatim:
The bank would like to recall a members credit card if the probability that a member will default is known to be greater than 0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?

I am unfamiliar with the word "defualt" in the context of credit cards. Does that mean the holder has failed to pay the balance too many times and can't use the card anymore?

Originally Posted by Jskid

The question verbatim:
The bank would like to recall a members credit card if the probability that a member will default is known to be greater than 0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?

I am unfamiliar with the word "defualt" in the context of credit cards. Does that mean the holder has failed to pay the balance too many times and can't use the card anymore?

Using the tree diagram suggested in post #2, $\displaystyle \displaystyle {\Pr(D \, | \, M) = \frac{0.05}{0.05 + (0.95)(0.2)} = .... }$ Therefore ....