please may you resolve the proplem a full answer thanks
please may you resolve the proplem a full answer thanks
Inthe1980s,random drug-testingpoliciesdesignedtoidentify individuals whowereusingillegaldrugs becamepopular within governmentand civilianorganiza- tions. Hereisasummary ofthefactscitedbytheleaderofafictitious “XYZorganiza- tion” tosupportsuchpolicies:
• Druguseisaseriousproblem for(XYZorganization)and wecannot tolerate drug userswithin ourranks. Consequently,Iwanteachdivisionleader tosendat least five individuals perweekforrandom drug testing. The test is99%accurate inidentifying drugusers. Nowwecanfindthedrugusersandseparate them fromtheorganization.
•99%ofourpeopledon’tusedrugs.
•There’snoplacein(XYZorganization)forthe1%whoaredrugusers. UsingBayes’Rule,evaluate theefficacyofsuchadrugtesting policy:
a)Assumeprior probabilitiesof1%fordrug usersand 99%fornon-drug userswithin the populationofXYZ.(The seniorleader said,1%ofthe XYZpopulationconsistsof drugusers).
b)A“positive” drugtestindicates thatanindividual islikelyadruguser. A“negative”
result indicates thattheindividual islikelynotadruguser.
c)Assumethatanindividual whoactually usesillegaldrugs willtest positive 99%of the time, and anon-drug usertests positive 1%ofthe time whenarandom drug test isadministered. Conversely, anon-drug userwilltest negative 99%ofthe time, and a
druguserwilltest negative 1%ofthetime.
d)Estimatethe probabilitythatanindividual isinfactadrug userifadrug test ad- ministered totheindividual results ina“positive.”
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