HungryHobo comments on If there was one element of statistical literacy that you could magically implant in every head, what would it be? - Less Wrong
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That when you've already picked someone/something out from the general population based on a particular property you cannot then use the same criteria to come to conclusions.
If you use a DNA matching technique with a 1 in a million chance of a false positive to pick your suspect out of a large database of people you cannot then use that "1 in a million chance" as part of the evidence against them. Yet courts absolutely would. (doing it the other way round, selecting one person then using the test is perfectly reasonable)