An athletic league does drug testing of its athletes, 15 percent of whom use dru
ID: 3202731 • Letter: A
Question
An athletic league does drug testing of its athletes, 15 percent of whom use drugs. This test, however, is only 97 percent reliable. That is, a drug user will test positive with probability 0.97 and negative with probability 0.03, and a nonuser will test negative with probably 0.97 and positive with probability 0.03. Use Bayes’ Theorem to determine the posterior probability of each of the following outcomes of testing an athlete: a)The athlete is a drug user, given that the test is positive. b) The athlete is not a drug user, given that the test the negative.
Explanation / Answer
P(athelete use drug) = 0.15
P(athelete does not use drug) = 0.85
P(test is positive) = 0.15*0.97 +0.85*0.03 = 0.171
P(test is negative) = 0.15*0.03+0.85*0.97 = 0.829
P(athlete is a drug user, given that the test is positive) = P(athlete is a drug user and test is positive)/P(test is positive)
= 0.15*0.97/0.171 = 0.85
P(athlete is not a drug user, given that the test the negative) = P(athlete is not a drug user and test is negative)/P(test is negative) = 0.85*0.97/0.829 = 0.99