Comment Bayesian thinking (Score 1) 365
There's a brilliant article that discusses this problem here: http://yudkowsky.net/rational/bayes. About a quarter of the way in there's a look at a few different ways of expressing the quantities. It seems frequencies are good (3 in every 1000 innocent people will be IDed as a terroist or 299 in every 300 people identified as a terrorist are innocent). People intuitively focus on the expected outcome - postive test result == terrorist and negative == not a terrorist. Maybe the way to make it clear is to tell them the non-intuitive statistics (299 in 300 that appear guilty are innocent while 1 in 30,000 that appear innocent are guilty). The issue is that if you tell someone "Q given P" (positive-result given is-terrorist) they always fall into the trap of thinking "P given Q" (is-terrorist given positive-result). Saying the test is 90% accurate is saying "Q given P 90% of the time". No one understands prior probability yet figures like this always ignore it.