Your company is implementing a new drug testing policy. The test you have chosen

Question

Your company is implementing a new drug testing policy. The test you have chosen has a 3% chance of resulting in false negatives, in other words, 3% of the time, the individual still passes the test even though they actually have taken banned drugs. The test you have chosen also has an 8% chance of resulting in false positives. In other words, 8% of the time, the test incorrectly shows the individual fails the test even though they actually have not taken banned drugs. If you assume that 1% of the employees actually take banned drugs, what is the probability of any one randomly selected employee passing test? How many individuals would you test each day to expect to find that fails the test?

Explanation / Answer

5.

Let

D = uses drugs
P = tests positive

Hence, by Bayes' Rule,

P(P) = P(D) P(P|D) + P(D') P(P|D') = 0.01*(1-0.03) + (1-0.01)*0.08 = 0.0889

Hence,

P(P') = 1 - P(P) = 0.9111 [ANSWER, probability that an individual passes the test]

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To find on who fails the test, we test on the average

E(n) = 1/P(P) = 11.24859 or around 11 individuals [ANSWER]

  

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