A loan officer is considering a loan request from a customer.

Base on the bank's records over years, there is an 8% chance that a

customer who has overdrawn an account will default on the loan.

However, there is only a 1% 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 O be the event that customer

overdraws his account, and let D be the event that the customer defaults

on the loan. Use tree diagram to answer b) and c).

a) Are the event of default on the loan independent of the event of overdraw?

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

c) Given that a customer has defaulted on his loan, what is the probability that he overdraws the account?

d) New information about the customer becomes available. If this new information indicates that there is only a 25% chance that this customer will overdraw his account, rather than a 40% chance, how does this change the answer in c)?