Question

According to the guidelines of the World Anti-Doping Agency (WADA), athletes are subject to testing both ‘in-competition’ and ‘out-of-competition’ for prohibited substances. Suppose that the tests for prohibited substances can identify a substance abuse 96% of the time. However, 2% of the time the test indicates a positive result although the athlete is not a prohibited substance user. If 5% of all athletes are users of prohibited substances, what is the probability that an athlete who has tested positive for a prohibited substance is not really a prohibited substance user? Round your answers to the nearest ten-thousandth (4 decimals).

Answer 1

Contingency table based on the information:

P(tested positive but not a user) = False positive / (True positive + false positive)

P(tested positive but not a user) = 0.019 / (0.019 + 0.048)

P(tested positive but not a user) = 0.2836