Question

Assume that a drug test is developed to detect steroid usage by amateur athletes. The test will accurately identify a steroid user 90% of the time. Unfortunately, it will generate a false positive 5% of the time. Assume the test is given to a thousand athletes where it is known that 0.1% are actual steroid users. If an athlete tests positive, what is the probability that he/she actually was using steroids

Answer 1

0.018

Explanation:

Probability of (The test will accurately identify a steroid user) = 90% = 0.9

Probability of (generating a false positive(probability of testing positive and he/she is not a steroid user)= 5% = 0.05

Probability of ( actual steroid users) = 0.1% = 0.001

Probability of not been a steroid user = 1 - 0.001 = 0.999

Probability that( he/she actually was using steroid and if an athlete tests positive) = 0.001 × 0.9 / 0.001 × 0.9 + 0.5 × 0.999

= 0.009/0.009 + 0.4995

= 0.009/0.5085

= 0.017699115

Approximately = 0.018