Federal banking laws require that commercial banks maintain

Federal banking laws require that commercial banks maintain an independent internal audit staff for the purpose of examining the controls and procedures used by each operating department. These periodic examinations must decide whether the department being examined is adhering to these controls or not. The auditors must also be on the look out for fraud. Aubrey has just started the audit of the commercial loan department of a bank. From previous experience, Aubrey believes there is a 90% chance that the department is adhering to current procedures and controls. Aubrey feels that if the department is in control, there is a 2% chance of uncovering an error during an examination of a commercial loan. If the department is not in control, there is a 50% chance of detecting an error in a commercial loan. If the department is in control, what is the chance that examination of a randomly selected commercial loan will yield an error? Suppose the department is in control. 6 unrelated and unconnected commercial loans are selected. What is the probability that at most 2 will be identified as having an error? A commercial loan is selected at random. It concerns a loan that was made a year ago and an error (a missing signature) is discovered. Given this piece of information, what is the probability that the commercial loan department is in control? Aubrey decides to examine another loan record. In this one, no mistakes are found. Now what is the probability that the department is in control? Another loan record is examined and again no error is found. Aubrey declares that he is satisfied that the department is in control. Given that out of three records, one is in error, should one continue to examine more files?

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