Drug use among air traffic controllers is discouraged and tests are conducted to

Question

Drug use among air traffic controllers is discouraged and tests are conducted to monitor drug use. The probability a particular urine test used to screen for drug use gives a positive reading is 0.85 in cases in which the person is a drug user, and the probability this test gives a positive reading is 0.12 in cases in which the person is not a drug user. It is thought that the probability of drug use among air traffic controllers is 0.007 (less than 1%). If an air traffic controller selected at random tests positive for drug use, what is the probability that the person selected actually IS a drug user? State your answer to 3 places of decimal.

Explanation / Answer

Let

D = drug user
P = tests positive

Hence,

P(P) = P(D) P(P|D) + P(D') P(P|D') = 0.007*0.85 + (1-0.007)*0.12 = 0.12511

Hence,

P(D|P) = P(D) P(P|D)/P(P) = 0.007*0.85/0.12511 = 0.047558149 = 0.048 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.