Inthe1980s,randomdrug-testingpoliciesdesignedtoidentify indi

Inthe1980s,randomdrug-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 inidentifyingdrugusers. Nowwecanfindthedrugusersandseparate them fromtheorganization.•99%ofourpeopledon’tusedrugs.•There’snoplacein(XYZorganization)forthe1%whoaredrugusers. UsingBayes’Rule,evaluate theefficacyofsuchadrugtesting policy:a)Assumepriorprobabilitiesof1%fordrug usersand 99%fornon-drug userswithin the populationofXYZ.(The seniorleader said,1%ofthe XYZpopulationconsistsof drugusers).b)A“positive” drugtestindicates thatanindividual islikelyadruguser. A“negative”result indicatesthattheindividual 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 adruguserwilltest negative 1%ofthetime.d)Estimatethe probabilitythatanindividual isinfactadrug userifadrug test ad- ministered totheindividual results ina“positive.”