4.76 Loan officer decision. A loan officer is con-
sidering a loan request from a customer of the bank.
Based on data collected from the bank’s 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?
TOPIC:Events and probability.
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