A bank classifies customers as either a good or bad credit risks. On the basis of extensive historical data, the bank has observed the following: • 5% of good credit risks overdraw their account in any given month. (In other words, given that a randomly chosen customer is a 'good credit risk', there is 5% chance that he/she will overdraw his/her account in any given month.) • 15% of bad credit risks overdraw their account in any given month. (In other words, given that a randomly chosen customer is a 'bad credit risk', there is 15% chance that he/she will overdraw his/her account in any given month.) A new customer opens a checking account at this bank. On the basis on a check with the credit bureau, the bank believes that there is a 70% chance that the customer is a good credit risk. Use the following notations: Let A be the event that the customer will overdraw his account. Let B be the event that the customer is a good credit risk. (a) The problem gives you three pieces of probability information. Write them down in terms of the events A and B. (b) Create a probability tree for this problem. (c) What is the probability that the customer overdraws his account in a given month. (d) Suppose that this customer's account is overdrawn in the first month. How does this alter the bank's opinion of this customer's creditworthiness? In other words, given that the customer's account is overdrawn, what is the proba- bility that the customer is a good credit risk.