Screening for disease and dishonesty

A secret government agency has developed a scanner which determines whether a person is a terrorist. The scanner is fairly reliable; 95% of all scanned terrorists are identified as terrorists, and 95% of all upstanding citizens are identified as such. An informant tells the agency that exactly one passenger of 100 aboard an aeroplane in which in you are seated is a terrorist. The agency decide to scan each passenger, and the shifty looking man sitting next to you tests positive. Were you sitting next to a terrorist? What are the chances that this man really is a terrorist?

Screening for breast cancer

Since 1988, women over 50 in the UK have routinely been offered screening for breast cancer, even if they have no other symptoms, and in 2004/05 1.7 million women were screened. Those with a positive mammogram are recalled for further investigations, at considerable cost in anxiety, resources and pain and discomfort. But how many of these women really have breast cancer?

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