Question

When IRS receives tax forms, it puts them through a computer to flag forms that need to be investigated further. The computer looks for mistakes in the forms, for example addition mistakes or incorrect deduction amounts. Suppose the computer correctly flags 80% of all returns that have mistakes, and it incorrectly flags 5% of error-free returns. Further, suppose that 15% of all tax returns have errors.

A tax return is flagged by the computer. What is the chance that it actually contains mistakes, given that the computer flagged it?

Answer 1

Let Ę = Return has an error F = Return as flacjged by computer Now, We need to calculate probability (Elp) Given, PCE) = 0.15 P(FIE) = 0.80 P(El not E) = 0.05 Cs Scanned with CamScanner

By cusing Bayes Rule, PCEF) = P(E and. F) PCF) P(FIE) (P(E)) P(F) - (0.80)(0.15) P(F) We know that, PCF) - PCF and 'E) + PC F and not E) = (0.80 )(0:15 )+ P (Finor E) P(not F) - (0.80)(0.15) +(005)(0.85) P(F) = 0.1625 So, PCEF) = 60-80 (0.15) 0.1625 -0.7385 . There is 73.55% chance that the return has an error, given that the computer flagged big increase from Note that this is 15% to 13.854 Soe the computer really helps identify erroneous CamScanngleturns.