An athletic league does drug testing of its athletes, 15 percent of whom use dru

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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