Dataanalystsoftenimplementstatisticalinferencemethodsbysettingtheprobabilityofa correct inferenceequalto0.95.Let A denote theeventthataninferenceforthepopulation aboutmeniscorrect.Let B representtheeventofacorrespondinginferenceaboutwomen beingcorrect.Supposethattheseareindependentevents.

(a) Findtheprobabilitythat(i) both inferences arecorrect,(ii) neither inference iscorrect.

(b) Constructtheprobabilitydistributionfor Y = numberofcorrectinferences.

(c) Withwhatprobabilitywouldeachinferenceneedtobecorrectinorderfortheprobability to be0.95that both are correct?