A passage from chapter 36 of Sam Savage’s excellent book The Flaw of Averages:
So how many true terrorists do you think are currently in the United States? … I have no idea myself, but for the sake of argument, suppose there are 3,000. That is, in the total U.S. population of 300 million, one person in 100,000 is the real deal.
Now consider a magic bullet for this threat: unlimited wiretapping tied to advanced voice analysis software on everyone’s phone line. The software can detect would-be terrorists within the utterance of three words … Assume that the system is 99 percent accurate; that is, if a true terrorist is on the line, it will notify the FBI 99 percent of the time, whereas for nonterrorists, it will call the FBI (in error) only 1 percent of the time. …
When the FBI gets a report from the system, what is the chance it will have a true terrorist?
f. One chance in 1,000
The answer is f: the system would turn up 2,970 terrorists and 2,999,970 false positives. The point that tightening up security procedures enough to catch the likes of Farouk Abdulmutallab would net lots and lots of harmless people has been made before, but Savage does demonstrate it quite elegantly, doesn’t he?