Test for certain type of drug usage (e.g., steroids) Test result is either “+” o
ID: 3045587 • Letter: T
Question
Test for certain type of drug usage (e.g., steroids)
Test result is either “+” or “-”
Tests are never perfect: false positives and false negatives
5% of all athletes use performance enhancing drugs (e.g., steroids)
3% of all tests on drug-free athletes yield false positives
7% of all tests on drug users yield false negatives
What is the probability of a “+” test?
What is the probability of a “-” test?
What is the probability an athlete is drug free given a “-” test result?
What is the probability an athlete uses drugs given a “+” test result?
What can we conclude from a positive or negative test result?
Is drug testing of athletes effective? Why or Why not?
Explanation / Answer
1) probability of a “+” test =P(+) =P(uses and test positive)+P(does not use and test positive)
=0.05*(1-0.07)+(1-0.05)*0.03=0.075
2) probability of a “-” test =1-P( positive test) =1-0.075 =0.925
3)probability an athlete is drug free given a “-” test result =P( dreg free and negative)/P(negative test)
=0.95*(1-0.03)/0.925=0.9962
4) probability an athlete uses drugs given a “+” test result =P(uses and test positive)/P(test positive)
=0.05*(1-0.07)/0.0725 =0.6414
5) we can colclude froom positive or negative test expectation of a person for being a frug user or not.
6)
as probability of being drug user given test is postiive is not very higher therefore testing is not very effective