homework02_2020
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SPRING2020
EconomicMathematicsII
PROBLEMSET#2
1.ForeventAandB,findformulafortheprobabilitiesofthefollowingeventsinterms
ofthequantitiesP(A),P(B),andP(A∩B):
(a)eitherAorBorboth;
(b)eitherAorBbutnotboth;
(c)atleastoneofAorB;
(d)atmostoneofAorB;
2.LetAandBbetwoevents.Checkifthefollowingrelationshold:
(a)A∪B=A∪(Ac∩B)?
(b)B=(A∩B)∪(Ac∩B)
Pleasegiveyourreasoningclearly.
3.SupposeeventsAandBaremutuallyexclusive.
(a)CanwesaythatAcandBcmutuallyexclusive?Giveyourreasoning.
(b)PleasefindsomeexamplesuchthatAcandBcaremutuallyexclusiveaswell?
4.ConsidertwoeventsAandBsuchthatP(A)=1/3andP(B)=1/2.Determinethe
valueofP(B∩Ac)foreachofthefollowingconditions:
(a)AandBaredisjoint;
(b)A⊂B;
(c)P(A∩B)=18.
5.SupposeP(A)=1/3andP(B)=1/4:IsitpossiblethatAandBaremutually
exclusive?
6.If50%ofthefamiliesinacitysubscribetothemorningnewspaper,65%ofthe
familiessubscribetotheafternoonnewspaper,and85%ofthefamiliessubscribetoat
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leastoneofthetwonewspapers,whatistheproportionofthefamiliessubscribetoboth
newspapers?
7.LetA,B,CbethreeeventsinSamplespaceS:ExpressP(A∪B∪C)intermsof
P(A),P(B),P(C),P(A∩B),P(B∩C),P(C∩A)andP(A∩B∩C).Giveyourreasoning.
8.(#2.26,p.51)ACaliforniastudyconcludedthatfollowing7simplehealthrulescan
extendamanslifeby11yearsontheaverageandawomanslifeby7years.These7
rulesareasfollows:nosmoking,getregularexercise,usealcoholonlyinmoderation,
get7to8hoursofsleep,maintainproperweight,eatbreakfast,anddonoteatbetween
meals.Inhowmanywayscanapersonadopt5oftheserulestofollow
(a)ifthepersonpresentlyviolatesall7rules?
(b)ifthepersonneverdrinksandalwayseatsbreakfast?
9.(#2.31,p.51)Awitnesstoahit-and-runaccidenttoldthepolicethatthelicense
numbercontainedthelettersRLHfollowedby3digits,thefirstofwhichwasa5.If
thewitnesscannotrecallthelast2digits,butiscertainthatall3digitsaredifferent,
findthemaximumnumberofautomobileregistrationsthatthepolicemayhavetocheck.
10.(#2.32,p.52)(a)Inhowmanywayscan6peoplebelineduptogetonabus?
(b)If3specificpersons,among6,insistonfollowingeachother,howmanywaysare
possible?(c)If2specificpersons,among6,refusetofolloweachother,howmanyways
arepossible?
11.(#2.33,p.52)Ifamultiple-choicetestconsistsof5questions,eachwith4possible
answersofwhichonly1iscorrect,(a)inhowmanydifferentwayscanastudentcheck
offoneanswertoeachquestion?(b)inhowmanywayscanastudentcheckoffone
answertoeachquestionandgetalltheanswerswrong?
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