exercise, you're the auditor. The directors of a large corporation suspect that some sales receipts have been incorrectly dated and some inventory levels have been overstated. ### Questions: * Explain why an auditor need only inspect a subset of transactions rather than census every transaction. * In order for the probability calculations to be simplified, how should the inventory items he chosen? * Suppose the corporation is divided into several sales divisions. The directors would like to simplify the gathering of sales records by picking one division at random. Would this be a good idea? For these calculations, assume that 2% of sales receipts have been date shifted and 3% of inventory levels have been overstated. * what is the probability that a random sample of 25 sales receipts will find none that are fraudulent? * what is the probability that a random sample of 25 sales receipts and 25 inventory counts will find at least one incident of fraud? * You can afford to audit a total of at most 13B sales receipts and inventory items. under these conditions, how many of each should you sample in order to maximize the chances of finding at least one fraudulent record? Are you satisfied with this result? * Suppose that checking a random sample of 25 sales receipts and 25 inventory counts finds no evidence of fraud. Does this mean that the probability of fraud at this company is zero? # Chapter 3 ## Key Terms Bayes' Rule conditional probability dependent events joint probability marginal probability Multiplication Rule probability tree {tree diagram} 131-1-131-131- ## Case 1: MANAGING A FHUCESE Breast cancer is the most common nonskin malignancy among women in the United States, and it is the second leading cause of death from cancer among women [lung cancer ranks first). A mammogram is a diagnostic procedure designed to quickly detect breast cancer. Such a test can exhibit two kinds of errors. one error is known as a false positive: The test incorrectly indicates cancer in a healthy woman. The other error {which is more serious error in this situation} is a false negative: The test fails to detect cancer. The probabilities of these errors are established in clinical trials. In a clinical trial, the test is applied to two groups of people, some known to be healthy and others known to have cancer {through an established test that is more complicated, time consuming, and expensive than the proposed new method}. Among women with breast