A credit card company has found that 0.1% of all transactions are fraudulent. It has developed a computer program that correctly
identifies whether a transaction is fraudulent or not 99% of the time. If the program scans 5,000,000 transactions, about how many of them will it identify as fraudulent?
Given: 0.1% of all transactions are fraudulent 99% correct identification whether a transaction is fraudulent or not. Scanned 5,000,000 transactions.
5,000,000 x 0.1% = 5,000 fraudulent transactions.
For me, there are 5,000 fraudulent transactions. This is based on the 0.1% rather than the 99%. Because the problem clearly states that the 0.1% of ALL transaction is identified as fraudulent. The 99% of the computer program only deals with the correct identification of the transaction as either fraudulent or not. For me, it is not a clear measure of the true number of fraudulent transactions.
An <em>inverse</em> function is any function that "undoes" another function. If we think of the function as some kind of machine that takes in a number as input and produces a number as an output, when we give inverse function the number as in input, we get , our original input, as the output
We need a function that undoes , and the natural choice for undoing an exponent is with a logarithm. Here, our base is , so we'll choose as our inverse function. Let's see how that works:
is the power we have to raise to to get , which is , so