Imagine you are the CEO of a local bank whose credit card holders engage in 1 billion credit card transactions per year; that the likelihood of a fraudulent transaction is 2%; that the average transaction purchase value for all transactions is equal to $38.50; and that the bank bears the full cost of all fraudulent transactions (i.e., you hold the cardholder harmless and lose the money yourself). A technology vendor proposes a software solution that will allow you to identify and decline 50% of all fraudulent transaction, thus reducing your fraudulent transaction rate to 1%. What is the maximum amount of money that you would be willing to pay for this investment? Why (please justify using mathematical/statistical tools)? What other information would be important to you in deciding whether the software is worth the investment?
Here is my answer:
At the rate of 1%, expected number of fraudulent transactions ...
The solution provides detailed explanation how to find the mean for the binomial probability distribution.