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@Thrustvector
Pretty sure Ben Goldacre talks about this in one of his books; I'd imagine he's discussed it on his blog somewhere. I think he used the example of a 99% specific/sensitive HIV test. Because the underlying rate of HIV in the population is so low, even if you get a positive result you're still more likely to have had a false positive than to actually have the disease. Statistics are counterintuitive and weird.
(Edit: I find visualisations help with this more than reading the explanations, i.e. 1000 squares coloured according to how many in the population actually have the disease, and how many the various tests will show up as positive/negative)