This article about false positives seems quite well done.
The BBC article links to an animation on the Understanding uncertainty website. I'm not sure if the animation is a good teaching aid - it shows the test being applied with a great random rattling of the faces of the 100 humans. I think it would be better to reveal the truth early so the viewer can understand the generative process, instead of it looking like every individual is being utterly randomized. I also find it confusing that colour (Red/green) is used initially to encode test result, then it is later used to encode the underlying truth. I think two different dimensions should have been used.
I'd reveal the truth, show the generative process, then hide the underlying truth to emulate "what the tester sees"; then reveal the truth again.
ps... I find it a bit uneasy-making that the whole set-up involves "detecting terrorists". The implicit endorsement of "war on terror"; the endorsement of the campaign to "be suspicious of your neighbours, look for stuff in their bins, and get them arrested and interrogated".
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