Air traffic controllers monitor the flights of aircraft and help to ensure safe

Question

Air traffic controllers monitor the flights of aircraft and help to ensure safe takeoffs and landings. In the US air traffic controllers are required to undergo periodic random drug testing. A urine test is used an initial screening test due to its low cost and ease of implementation. One such urine test, the Triage Panel for Drugs of Abuse plus TCA, detects the presence of drugs and has a sensitivity of 0.96 and a specificity of 0.93. Based on past drug testing of air traffic controllers, the FAA reports that the probability of drug use is 0.007. Use this information to answer the next 2 questions.

part a) What is the probability that an air traffic controller returns a positive drug test?

a) 0.0067

b) 0.007

c) 0.0695

d) 0.0762

e) None of the above are close

part b) Given that an air traffic controller returns a positive drug test, what is the probability that they have been using drugs?

a) 0.007

b) 0.088

c) 0.912

d) 0.96

e) None of the above are close

Explanation / Answer

1)probability that an air traffic controller returns a positive drug test=P(D)*P(+ve|D)+P(ND)*P(+ve|ND)

=0.007*0.96+0.993*0.07=0.07623

option D

2)probability that they have been using drugs, given returns a positive drug test=P(D)*P(+ve|D)/P(+ve)

=0.007*0.96/0.07623=0.088154

option B

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