3. Athletes in high level competitions like the Olympics are subject to urine dr

Question

3. Athletes in high level competitions like the Olympics are subject to urine drug tests (UDT's) for the use of banned substances. False positives can occur from in vivo metabolic conversions of a legal substance, exposure to nonillicit sources, or laboratory error. False negative UDT results include limited assay specificity, absence of the substanoe in the urine, or laboratory error. Let A be the event tests positive and C be the event the athlete used a banned substance. a) Given a false positive rate of 1% and a false negative rate of 0.5%, find P(AC) and P(AC) b Find the probability that an athlete tests positive if the fraction of athletes that use a banned substance is 2%. c) Find the probability that an athlete used the drug given that the test is positive. d) What would have a bigger impact on this probability, reduction in fialse positive probability or false segative probabiity? Explain your answer.

Explanation / Answer

a)P(A|C) =probability of test positive given used banned substance =1-false negative =1-0.005 =0.995

P(A|Cc) =probability of test positive given not used banned substance =false positive =0.01

b) P(A) =P(C)*P(A|C)+P(Cc)*P(A|Cc) =0.02*0.995+(1-0.02)*0.01 =0.0297

c)P(C|A)= P(C)*P(A|C)/P(A)=0.02*0.995/0.0297=0.6700

d)reduction in false positve will have greater impact; as weigtage of its (proportion of those who are not using banned drugs) is higher which will impact overall probability more,

please revert for any clarification required

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