Solution to Problem 94

Congratulations to this week's winner

Andrew Hess

Other correct solutions were sent in by Josh Durham, Mundia Mubyana, Ray Kremer. Further correct solutions were submitted by Jens Voss, Burkart Venzke, Rick Honsinger, Brian Laughlin, Ahron Teitelman, Guy Forrester, Philippe Fondanaiche, Ariel Flat.

Of the 5000 employees in the company 5%, or 250 people, will be drug users, while the remaining 4750 will be non-drug users. The test will yield a positive result for 99% of the drug users, which amounts to 247.5 people (however you want to interpret that), as it will for 1% of the non-drug users, which amount to 47.5 people. The total number of positive results will be 247.5 + 47.5 = 295, of which only 247.5, or about 83.9%, are actually drug users.

Using the logic above, to get a test that will correctly identify 99% of drug users, the test would have to be 99.947% accurate.

Andrew Hess points out that the number of employees in the company is irrelevant to the problem.

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Page last updated 12 October 2000.