Credit-card fraud costs business in the United States billions of dollars each year in stolen goods. Compounding the problem, the risk of fraud increases with the rapidly growing online retail market. To reduce fraud, businesses and credit card vendors have devised systems that recognize characteristics of fraudulent transactions. These systems are not perfect, however, and sometimes fag honest transactions as fraudulent and sometimes miss fraudulent transactions.
A business has been offered a fraud detection system to protect its online retail site. The system promises very high accuracy. The system catches 99% of fraudulent transactions; that is, given a transaction is fraudulent, the system signals a problem 99% of the time. The system fags honest transactions as fraudulent only 2% of the time.
(a) What would be possible consequences to the retailer of mistaking honest transactions for fraudulent transactions? Mistaking fraudulent transactions for honest transactions?
(b) The description of this system gives several conditional probabilities, but are these the conditional probabilities that are most relevant to owners of the retail site? What other probabilities would be helpful?
(c) Suppose that the prevalence of fraud among transactions at the retailer is 1%. What are the chances that the system incorrectly labels honest transactions as fraudulent?
(d) Suppose that the prevalence of fraud is higher, at 5%. How does the performance of this system change?
(e) Summarize your evaluation of this system for the retailer. Do you think that this system will be adequate for its needs?