Suppose a student needs to apply for a loan to enroll at the University of Melbourne, Australia. She believes that there is a 0.8 probability that the loan will be approved within the next three months if the bank interest rate remains the same, and a 0.4 probability that the loan will be approved within the next three months if the interest rates change. A bank manager believes that there is 0.65 probability that the interest rate will remain the same in the next three months.

a. What is the probability that the student’s loan will be approved by the bank within the next three months?

b. If there is a 0.75 probability to get the loan, what is the probability that the bank interest rate will remain the same?