Question

A loan officer is considering a loan request from a customer of the bank. Based on data collected from the banks records over many years, there is an 8% chance that a customer who has overdrawn an account will default on the loan. However, there is only a 0:6% chance that a customer who has never overdrawn an account will default on the loan. Based on the customer’s credit history, the loan officer believes there is a 40% chance that this customer will overdraw his account. Let D be the event that the customer defaults on the loan, and let O be the event that the customer overdraws his account.

(a) Express the three probabilities given in the problem in the notation of probability and conditional probability.

(b) What is the probability that the customer will default on the loan?

Answer 1