7. When you submit your tax return to the IRS,they screen your return for indications of fraud. Naturally thescreening system is not perfect: only 92% of fraudulent tax returnsget red-flagged (that is, the IRS’ system detects the fraud), and9% of honest tax returns get red-flagged (the system mistakenlybelieves these good returns to be fraudulent). A tax return the IRSbelieves not to be fraudulent is said to be “green-flagged.”Suppose that 4% of all tax returns are fraudulent.(a) What percent of all tax returns are correctlyflagged?
(b) If a tax return is red-flagged, what is theprobability this return is fraudulent?
(c) The answer to part (b) might worry anadministrator at the IRS (or a taxpayer, for that matter!). Brieflyexplain what causes the answer to part (b) to be somewhat low.
