Suppose there is a new computer virus, H1NQ, which is both polymorphic and metamorphic. Mike has a new malware-detection program, QSniffer, that is 95% accurate at detecting H1NQ. That is, if a computer is infected with H1NQ, then QSniffer will correctly detect this fact 95% of the time, and if a computer is not infected, then QSniffer will correctly detect this fact 95% of the time. It turns out
that the H1NQ virus will only infect any given computer with a probability of 1%. Nevertheless, you are nervous and run QSniffer on your computer, and it unfortunately says that your computer is infected with H1NQ. What is the probability that your computer really is infected?
What will be an ideal response?
Think of a campus of 2000 computers. By the properties of H1NQ, 20 of these
computers are (randomly) infected with H1NQ. QSniffer will correctly identify 19 of these
as infected. But of the 1980 uninfected computers, QSniffer will say that 99 of them are
infected when they are not. Thus, if QSniffer were run on all 2000 computers, it would say
that 19+99 = 118 of them are infected, but only 19 of them really are. Therefore, if it says
your computer is infected, there is a probability of 19/118 that it is right, which is about a
16,1% chance.
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