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Here’s your drug test, Minister…

Luckily for bookmakers, probability is not reliably intuitive. What is the value of a random drug test? (No account is taken here of the legality or morality of the testing).

Possibly not much. See Example 2 HERE.

The Wikipedia writer concludes that, even with the positive result for a test 99% sensitive and 99% specific, it is still more likely that the person tested and testing positive, is not a drug user than that he/she is a drug user.

The reason lies in the context of the drug testing. It occurs as a random test where the likelihood of encountering a drug user is known and is, in the example, .5%. So, a positive result even for a test as accurate as the postulated test is not affirmative, even probably, of drug use.

Hmm, what is .5% of a Cabinet?