Ch.3 Probability
3.1 BasicConceptsofProbabilityandCounting
1 FindProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Acoinistossed.Findtheprobabilitythattheresultisheads.
A) 0.5 B) 0.1 C) 0.9 D) 1
2) Asinglesix–sideddieisrolled.Findtheprobabilityofrollinganumberlessthan3.
A) 0.333 B) 0.1 C) 0.5 D) 0.25
3) Asinglesix–sideddieisrolled.Findtheprobabilityofrollingaseven.
A) 0 B) 0.1 C) 0.5 D) 1
4) Astudyof1000randomlyselectedflightsofamajorairlineshowedthat798 oftheflightsarrivedontime.
Whatistheprobabilityofaflightarrivingontime?
A) 399
500 B) 101
500 C) 500
101 D) 500
399
5) Ifonecardisdrawnfromastandarddeckof52playingcards,whatistheprobabilityofdrawinganace?
A) 1
13 B) 1
52 C) 1
4D) 1
2
6) Ifonecardisdrawnfromastandarddeckof52playingcards,whatistheprobabilityofdrawingaredcard?
A) 1
2B) 1
52 C) 1
4D) 1
13
7) Ifonecardisdrawnfromastandarddeckof52playingcards,whatistheprobabilityofdrawingaheart?
A) 1
4B) 1
2C) 3
4D) 1
8) Inasurveyofcollegestudents,840saidthattheyhavecheatedonanexamand1765saidthattheyhavenot.If
onecollegestudentisselectedatrandom,findtheprobabilitythatthestudenthascheatedonanexam.
A) 168
521 B) 353
521 C) 521
168 D) 521
353
9) Ifanindividualisselectedatrandom,whatistheprobabilitythatheorshehasabirthdayinJuly?Ignoreleap
years.
A) 31
365 B) 1
365 C) 364
365 D) 12
365
Page64
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
10) ThedatainthetablerepresentthenumberofconsumercomplaintsagainstmajorU.S.airlines.Ifonecomplaint
fromthetableisrandomlyselected,findtheprobabilitythatitwasfiledagainstUnitedAirlines.
Airline NumberofComplaints
United 1172
Northwest 765
Continental 563
11) ThedatainthetablerepresentthenumberofconsumercomplaintsagainstmajorU.S.airlines.Ifonecomplaint
fromthetableisrandomlyselected,findtheprobabilitythatitwasfiledagainstNorthwestAirlines.
Airline NumberofComplaints
United 1172
Northwest 765
Continental 563
12) ThedatainthetablerepresentthenumberofconsumercomplaintsagainstmajorU.S.airlines.Ifonecomplaint
fromthetableisrandomlyselected,findtheprobabilitythatitwasfiledagainstContinentalAirlines.
Airline NumberofComplaints
United 1172
Northwest 765
Continental 563
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
13) Thedistributionofbloodtypesfor100Americansislistedinthetable.Ifonedonorisselectedatrandom,find
theprobabilityofselectingapersonwithbloodtypeA+.
BloodType O+O–A+A–B+B–AB+AB–
Number 37 6 34 6 10 2 4 1
A) 0.34 B) 0.4 C) 0.45 D) 0.68
14) Thedistributionofbloodtypesfor100Americansislistedinthetable.Ifonedonorisselectedatrandom,find
theprobabilityofselectingapersonwithbloodtypeA+orA–.
BloodType O+O–A+A–B+B–AB+AB–
Number 37 6 34 6 10 2 4 1
A) 0.4 B) 0.34 C) 0.02 D) 0.06
15) Thedistributionofbloodtypesfor100Americansislistedinthetable.Ifonedonorisselectedatrandom,find
theprobabilityofnotselectingapersonwithbloodtypeB+.
BloodType O+O–A+A–B+B–AB+AB–
Number 37 6 34 6 10 2 4 1
A) 0.90 B) 0.82 C) 0.12 D) 0.10
Page65
16) Thedistributionofbloodtypesfor100Americansislistedinthetable.Ifonedonorisselectedatrandom,find
theprobabilityofselectingapersonwithbloodtypeAB–.
BloodType O+O–A+A–B+B–AB+AB–
Number 37 6 34 6 10 2 4 1
A) 0.01 B) 0.05 C) 0.99 D) 0.10
17) ThedistributionofMasterʹsdegreesconferredbyauniversityislistedinthetable.
Major Frequency
Mathematics 216
English 207
Engineering 63
Business 176
Education 222
WhatistheprobabilitythatarandomlyselectedstudentgraduatingwithaMasterʹsdegreehasamajorof
Engineering?Roundyouranswertothreedecimalplaces.
A) 0.071 B) 0.929 C) 0.016 D) 0.984
18) ThedistributionofMasterʹsdegreesconferredbyauniversityislistedinthetable.
Major Frequency
Mathematics 216
English 207
Engineering 86
Business 176
Education 267
WhatistheprobabilitythatarandomlyselectedstudentgraduatingwithaMasterʹsdegreehasamajorof
Education?Roundyouranswertothreedecimalplaces.
A) 0.280 B) 0.720 C) 0.004 D) 0.390
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
19) Usethefollowinggraph,whichshowsthetypesofincidentsencounteredwithdriversusingcellphones,to
findtheprobabilitythatarandomlychosenincidentinvolvescuttingoffacar.Roundyouranswertothree
decimalplaces.
Page66
20) Usethefollowinggraph,whichshowsthetypesofincidentsencounteredwithdriversusingcellphones,to
findtheprobabilitythatarandomlychosenincidentdidnotinvolvecuttingoffacar.Roundyouranswerto
threedecimalplaces.
21) Usethepiechart,whichshowsthenumberofCongressionalMedalofHonorrecipientsintheUnitedStates,to
findtheprobabilitythatarandomlychosenrecipientservedintheNavy.
22) Usethepiechart,whichshowsthenumberofCongressionalMedalofHonorrecipientsintheUnitedStates,to
findtheprobabilitythatarandomlychosenrecipientdidnotserveintheMarines.
Page67
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
23) Aquestionhasfivemultiple–choiceanswers.Findtheprobabilityofguessinganincorrectanswer.
A) 4
5B) 5
2C) 1
5D) 3
5
24) Aquestionhasfivemultiple–choicequestions.Findtheprobabilityofguessingthecorrectanswer.
A) 1
5B) 5
4C) 4
5D) 2
5
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
25) ThedistributionofMasterʹsdegreesconferredbyauniversityislistedinthetable.
Major Frequency
Mathematics 216
English 207
Engineering 86
Business 176
Education 222
FindtheprobabilityofrandomlychoosingapersongraduatingwithaMasterʹsdegreewhodidnotmajorin
Education.Roundyouranswertothreedecimalplaces.
26) ThedatainthetablerepresentthenumberofconsumercomplaintsagainstmajorU.S.airlines.Ifonecomplaint
fromthetableisrandomlyselected,findtheprobabilitythatitwasnotfiledagainstContinentalAirlines.
(Roundtothreedecimalplaces.)
Airline NumberofComplaints
United 287
Northwest 256
Continental 243
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
27) Astem–and–leafplotforthenumberofhomerunshitby30HighSchoolteamsisshown.Findtheprobability
thatateamchosenatrandomhitmorethan28homeruns.
Key:28
=28
1
2
3
4
5
89
023347889
11345568999
223569
15
A) 0.667 B) 0.233 C) 0.933 D) 0.509
2 IdentifytheSampleSpace
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Identifythesamplespaceoftheprobabilityexperiment:shootingafreethrowinbasketball.
2) Identifythesamplespaceoftheprobabilityexperiment:answeringatrueorfalsequestion
Page68
3) Identifythesamplespaceoftheprobabilityexperiment:recordingthenumberofdaysitsnowedinCleveland
inthemonthofJanuary.
4) Identifythesamplespaceoftheprobabilityexperiment:answeringamultiplechoicequestionwithA,B,C,and
Dasthepossibleanswers
5) Identifythesamplespaceoftheprobabilityexperiment:determiningthechildrenʹsgenderforafamilyofthree
children(UseBforboyandGforgirl.)
6) Identifythesamplespaceoftheprobabilityexperiment:rollingasingle12–sideddiewithsidesnumbered1–12
7) Identifythesamplespaceoftheprobabilityexperiment:rollingapairof12 –sideddice(withsidesnumbered
1–12)andobservingthetotalnumberofpointsofeachroll
8) Identifythesamplespaceoftheprobabilityexperiment:Acalculatorhasafunctionbuttontogeneratea
randomintegerfrom–5to5
9) Identifythesamplespaceoftheprobabilityexperiment:recordingaresponsetothesurveyquestionandthe
genderoftherespondent.
10) Identifythesamplespaceoftheprobabilityexperiment:recordingthedayoftheweekandwhetherornotit
rains.
Page69
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
11) Asportsteamhasathreegameroadtrip.Usethetreediagramtoanswerthequestion.
Listtheoutcome(s)oftheeventʺTheywinexactlytwogames.ʺ
A) {WWL,WLW,LWW} B) {WWW,WWL,WLW,LWW}
C) {WLL,LWL,LLW} D) {WWL,WLW}
Page70
12) Asportsteamhasathreegameroadtrip.Usethetreediagramtoanswerthequestion.
Listtheoutcome(s)oftheeventʺTheyloseatleastonegame.ʺ
A) {WWL,WLW,WLL,LWW,LWL,LLW,LLL} B) {WWL,WLW,LWW}
C) {WWW,WWL,WLW,WLL,LWW,LWL,LLW} D) {WWW,WWL,WLW,LWW}
3 IdentifySimpleEvents
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Determinethenumberofoutcomesintheevent.Thendecidewhethertheeventisasimpleeventornot.Explainyour
reasoning.
1) Acomputerisusedtorandomlyselectanumberbetween1and1000.EventAisselectinganumbergreater
than600.
A) 400;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
B) 1;Simpleeventbecauseitisaneventthatconsistsofasingleoutcome.
C) 600;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
D) 400;Simpleeventbecauseonlyonenumberisselected.
2) Yourollasix–sideddie.EventBisrollinganevennumber.
A) 3;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
B) 1;Simpleeventbecauseitisaneventthatconsistsofasingleoutcome.
C) 2;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
D) 3;Simpleeventbecausethedieisonlyrolledonce.
3) Yourandomlyselectonecardfromastandarddeck.EventBisselectingtheaceofhearts.
A) 1;Simpleeventbecauseitisaneventthatconsistsofasingleoutcome.
B) 4;Simpleeventbecauseonlyonecardisselected.
C) 4;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
D) 13;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
Page71
4) Yourandomlyselectacomputerfromabatchof50whichcontains3defectivecomputers.EventBisselectinga
defectivecomputer.
A) 3;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
B) 3;Simpleeventbecauseitisaneventthatconsistsofonlyonetypeofcomputer.
C) 1;Simpleeventbecauseitisaneventthatconsistsofonlyonetypeofcomputer.
D) 50;Notasimpleeventbecauseitisaneventthatconsistsofmorethanasingleoutcome.
4 UseFundamentalCountingPrinciple
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Usethefundamentalcountingprincipletosolvetheproblem.
1) Ashirtcompanyhas4designseachofwhichcanbemadewithshortorlongsleeves.Thereare5 colorpatterns
available.Howmanydifferentshirtsareavailablefromthiscompany?
A) 40 B) 20 C) 9 D) 11
2) If12newbornbabiesarerandomlyselected,howmanydifferentgendersequencesarepossible?
A) 4096 B) 24 C) 479,001,600 D) 144
3) Asinger–songwriterwishestocomposeamelody.Eachnoteinthemelodymustbeoneofthe12 notesinher
vocalrange.Howmanydifferentsequencesof3notesarepossible?
A) 1728 B) 531,441 C) 36 D) 1320
4) Howmanylicenseplatescanbemadeconsistingof3 lettersfollowedby2 digits?
A) 1,757,600 B) 100,000 C) 11,881,376 D) 175,760
5) Howmanydifferentcodesof4digitsarepossibleifthefirstdigitmustbe3,4,or5andifthecodemaynotend
in0?
A) 2700 B) 300 C) 2999 D) 3000
5 ClassifyTypesofProbability
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Classifythestatementasanexampleofclassicalprobability,empiricalprobability,orsubjectiveprobability.
Theprobabilitythatatrainwillbeinanaccidentonaspecificrouteis1%.
A) empiricalprobability B) classicalprobability C) subjectiveprobability
2) Classifythestatementasanexampleofclassicalprobability,empiricalprobability,orsubjectiveprobability.
Theprobabilitythatinterestrateswillriseduringthesummeris0.05.
A) subjectiveprobability B) classicalprobability C) empiricalprobability
3) Classifythestatementasanexampleofclassicalprobability,empiricalprobability,orsubjectiveprobability.
InCaliforniaʹsPickThreelottery,apersonselectsa3–digitnumber.TheprobabilityofwinningCaliforniaʹs
PickThreelotteryis 1
1000 .
A) classicalprobability B) empiricalprobability C) subjectiveprobability
4) Classifythestatementasanexampleofclassicalprobability,empiricalprobability,orsubjectiveprobability.
Theprobabilitythatanewbornbabyisaboyis1
2.
A) classicalprobability B) empiricalprobability C) subjectiveprobability
Page72
5) Classifythestatementasanexampleofclassicalprobability,empiricalprobability,orsubjectiveprobability.
Theprobabilitythatitwillraintomorrowis63%.
A) subjectiveprobability B) classicalprobability C) empiricalprobability
6 DetermineOdds
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) TheP(A)=3
5.FindtheoddsofwinninganA.
A) 3:2 B) 2:3 C) 3:5 D) 5:2
2) Acardispickedatrandomfromastandarddeckof52playingcards.Findtheoddsthatitisnotaheart.
A) 3:1 B) 1:3 C) 4:1 D) 1:4
3) Atthelocalracetrack,thefavoriteinaracehasodds3:2ofwinning.Whatistheprobabilitythatthefavorite
winstherace?
A) 0.6 B) 0.4 C) 0.2 D) 1.5
4) Atthelocalracetrack,thefavoriteinaracehasodds3:2oflosing.Whatistheprobabilitythatthefavoritewins
therace?
A) 0.4 B) 0.6 C) 0.2 D) 0.67
7 Concepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Whichofthefollowingcannotbeaprobability?
A) –19 B) 0 C) 0.001 D) 7
3
2) Whichofthefollowingcannotbeaprobability?
A) 4
3B) 0.0002 C) 1 D) 85%
3) Ranktheprobabilitiesof10%,1
5,and0.06fromtheleastlikelytooccurtothemostlikelytooccur.
A) 0.06,10%,1
5B) 1
5,10%,0.06 C) 0.06,1
5,10% D) 10%,1
5,0.06
4) Ranktheprobabilitiesof10%,1
5,and0.06fromthemostlikelytooccurtotheleastlikelytooccur.
A) 1
5,10%,0.06 B) 0.06,10%,1
5C) 10%,1
5,0.06 D) 0.06,1
5,10%
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
5) Explainwhythefollowingstatementisincorrect:
Hegave110%effort.
Page73
3.2 ConditionalProbabilityandtheMultiplicationRule
1 DetermineBetweenIndependentandDependentEvents
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Classifytheeventsasdependentorindependent.EventsAandBwhere
P(A)=0.8,P(B)=0.2,andP(AandB)=0.16
A) independent B) dependent
2) Classifytheeventsasdependentorindependent.EventsAandBwhere
P(A)=0.8,P(B)=0.8,andP(AandB)=0.63
A) dependent B) independent
3) Classifytheeventsasdependentorindependent.
Theeventsofgettingtwoaceswhentwocardsaredrawnfromadeckofplayingcardsandthefirstcardis
replacedbeforethesecondcardisdrawn.
A) independent B) dependent
4) Classifytheeventsasdependentorindependent.Theeventsofgettingtwoaceswhentwocardsaredrawn
fromadeckofplayingcardsandthefirstcardisnotreplacedbeforethesecondcardisdrawn.
A) dependent B) independent
5) Classifytheeventsasdependentorindependent.EventA:Aredcandyisselectedfromapackagewith30
coloredcandiesandeaten.EventB:Abluecandyisselectedfromthesamepackageandeaten.
A) dependent B) independent
2 FindConditionalProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Agroupofstudentswereaskediftheycarryacreditcard.Theresponsesarelistedinthetable.
Class
CreditCard
Carrier
NotaCreditCard
Carrier Total
Freshman 40 20 60
Sophomore 25 15 40
Total 65 35 100
Ifastudentisselectedatrandom,findtheprobabilitythatheorsheownsacreditcardgiventhatthestudentis
afreshman.Roundyouranswertothreedecimalplaces.
A) 0.667 B) 0.333 C) 0.615 D) 0.400
Page74
2) Agroupofstudentswereaskediftheycarryacreditcard.Theresponsesarelistedinthetable.
Class
CreditCard
Carrier
NotaCreditCard
Carrier Total
Freshman 11 49 60
Sophomore 6 34 40
Total 17 83 100
Ifastudentisselectedatrandom,findtheprobabilitythatheorsheownsacreditcardgiventhatthestudentis
asophomore.Roundyouranswertothreedecimalplaces.
A) 0.150 B) 0.850 C) 0.353 D) 0.060
3) Agroupofstudentswereaskediftheycarryacreditcard.Theresponsesarelistedinthetable.
Class
CreditCard
Carrier
NotaCreditCard
Carrier Total
Freshman 49 11 60
Sophomore 12 28 40
Total 61 39 100
Ifastudentisselectedatrandom,findtheprobabilitythatheorsheisafreshmangiventhatthestudentowns
acreditcard.Roundyouranswerstothreedecimalplaces.
A) 0.803 B) 0.817 C) 0.197 D) 0.490
4) Agroupofstudentswereaskediftheycarryacreditcard.Theresponsesarelistedinthetable.
Class
CreditCard
Carrier
NotaCreditCard
Carrier Total
Freshman 21 39 60
Sophomore 18 22 40
Total 39 61 100
Ifastudentisselectedatrandom,findtheprobabilitythatheorsheisasophomoregiventhatthestudent
ownsacreditcard.Roundyouranswerstothreedecimalplaces.
A) 0.462 B) 0.538 C) 0.975 D) 0.180
5) Agroupofstudentswereaskediftheycarryacreditcard.Theresponsesarelistedinthetable.
Class
CreditCard
Carrier
NotaCreditCard
Carrier Total
Freshman 28 32 60
Sophomore 10 30 40
Total 38 62 100
Ifastudentisselectedatrandom,findtheprobabilitythatheorsheisasophomoreandownsacreditcard.
Roundyouranswerstothreedecimalplaces.
A) 0.100 B) 0.737 C) 0.950 D) 0.263
Page75
3 UsetheMultiplicationRuletoFindProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Youaredealttwocardssuccessivelywithoutreplacementfromastandarddeckof52playingcards.Findthe
probabilitythatthefirstcardisatwoandthesecondcardisaten.Roundyouranswertothreedecimalplaces.
A) 0.006 B) 0.994 C) 0.250 D) 0.500
2) Findtheprobabilityofansweringtwotrueorfalsequestionscorrectlyifrandomguessesaremade.Onlyoneof
thechoicesiscorrect.
A) 0.25 B) 0.5 C) 0.75 D) 0.1
3) Findtheprobabilityofansweringthetwomultiplechoicequestionscorrectlyifrandomguessesaremade.
Assumethequestionseachhavefivechoicesfortheanswer.Onlyoneofthechoicesiscorrect.
A) 0.04 B) 0.004 C) 0.4 D) 0.02
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
4) Findtheprobabilityofgettingfourconsecutiveaceswhenfourcardsaredrawnwithoutreplacementfroma
standarddeckof52playingcards.
5) Findtheprobabilityofselectingtwoconsecutivethreeswhentwocardsaredrawnwithoutreplacementfroma
standarddeckof52playingcards.Roundyouranswertofourdecimalplaces.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
6) Amultiple–choicetesthasfivequestions,eachwithfivechoicesfortheanswer.Onlyoneofthechoicesis
correct.Yourandomlyguesstheanswertoeachquestion.Whatistheprobabilitythatyouanswerthefirsttwo
questionscorrectly?
A) 0.04 B) 0.2 C) 0.02 D) 0.4
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
7) Amultiple–choicetesthasfivequestions,eachwithfivechoicesfortheanswer.Onlyoneofthechoicesis
correct.Yourandomlyguesstheanswertoeachquestion.Whatistheprobabilitythatyouanswerallfive
questionscorrectly?
8) Amultiple–choicetesthasfivequestions,eachwithfivechoicesfortheanswer.Onlyoneofthechoicesis
correct.Yourandomlyguesstheanswertoeachquestion.Whatistheprobabilitythatyoudonotanswerany
ofthequestionscorrectly?
9) Amultiple–choicetesthasfivequestions,eachwithfivechoicesfortheanswer.Onlyoneofthechoicesis
correct.Yourandomlyguesstheanswertoeachquestion.Whatistheprobabilitythatyouansweratleastone
ofthequestionscorrectly?
10) Theprobabilityitwillrainis40%eachdayoverathree–dayperiod.Whatistheprobabilityitwillrainatleast
oneofthethreedays?
11) Theprobabilityitwillrainis40%eachdayoverathree–dayperiod.Whatistheprobabilityitwillnotrainat
leastoneofthethreedays?
Page76
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
12) Fourstudentsdrivetoschoolinthesamecar.Thestudentsclaimtheywerelatetoschoolandmissedatest
becauseofaflattire.Onthemakeuptest,theinstructorasksthestudentstoidentifythetirethatwentflat;front
driverʹsside,frontpassengerʹsside,reardriverʹsside,orrearpassengerʹsside.Ifthestudentsdidnʹtreallyhave
aflattireandeachrandomlyselectsatire,whatistheprobabilitythatallfourstudentsselectthesametire?
A) 1
64 B) 1
4C) 1
256 D) 1
8
13) Findtheprobabilitythatof25randomlyselectedstudents,notwosharethesamebirthday.
A) 0.431 B) 0.995 C) 0.569 D) 0.068
14) Findtheprobabilitythatof25randomlyselectedstudents,atleasttwosharethesamebirthday.
A) 0.569 B) 0.068 C) 0.432 D) 0.995
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
15) Whatistheprobabilitythatahusband,wife,anddaughterhavethesamebirthday?
4UseBayesʹsTheorem
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) UseBayesʹtheoremtosolvethisproblem.Astoreownerpurchasesstereosfromtwocompanies.From
CompanyA,650stereosarepurchasedand10%arefoundtobedefective.FromCompanyB,950stereosare
purchasedand2%arefoundtobedefective.Giventhatastereoisdefective,findtheprobabilitythatitcame
fromCompanyA.
A) 65
84 B) 95
84 C) 13
84 D) 19
84
2) UseBayeʹsTheoremtosolvethisproblem,Apaperbagcontainstworedballsandoneblueball.Aplasticbag
containsthreeblueballsandoneredball.Acoinistossed.Ifitfallsheadsup,thepaperbagisselectedanda
ballisdrawn.Ifthecoinfallstailsup,theplasticbagisselectedandaballisdrawn.Ifaredballisselected,
whatistheprobabilitythatitcamefromthepaperbag?
A) 8
11 B) 1
3C) 1
8D) 3
8
3.3 TheAdditionRule
1 DetermineifEventsAreMutuallyExclusive
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.Adieisrolled.
A:Theresultisanoddnumber.
B:Theresultisanevennumber.
A) mutuallyexclusive B) notmutuallyexclusive
2) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive,Adieisrolled.
A:Theresultisa3.
B:Theresultisanoddnumber.
A) notmutuallyexclusive B) mutuallyexclusive
Page77
3) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.AdateinPhiladelphiais
selected.
A:Itrainsthatday.
B:Itsnowsthatday.
A) notmutuallyexclusive B) mutuallyexclusive
4) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.Acardisdrawnfromastandard
deckof52playingcards.
A:Theresultisa7.
B:Theresultisajack.
A) mutuallyexclusive B) notmutuallyexclusive
5) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.Acardisdrawnfromastandard
deckof52playingcards.
A:Theresultisaclub.
B:Theresultisaking.
A) notmutuallyexclusive B) mutuallyexclusive
6) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.Apersonisselectedatrandom.
A:Theirbirthdayisinthefall.
B:TheirbirthdayisinOctober.
A) notmutuallyexclusive B) mutuallyexclusive
7) DecideiftheeventsAandBaremutuallyexclusiveornotmutuallyexclusive.Astudentisselectedatrandom.
A:Thestudentistakingamathcourse.
B:Thestudentisabusinessmajor.
A) notmutuallyexclusive B) mutuallyexclusive
2 UsetheAdditionRuletoFindProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Acardisdrawnfromastandarddeckof52playingcards.Findtheprobabilitythatthecardisanaceoraking.
A) 2
13 B) 1
13 C) 4
13 D) 8
13
2) Acardisdrawnfromastandarddeckof52playingcards.Findtheprobabilitythatthecardisanaceoraheart.
A) 4
13 B) 7
52 C) 17
52 D) 3
13
3) Acardisdrawnfromastandarddeckof52playingcards.Findtheprobabilitythatthecardisanaceorablack
card.
A) 7
13 B) 15
26 C) 29
52 D) 4
13
4) TheeventsAandBaremutuallyexclusive.IfP(A)=0.1 andP(B)=0.3
,
whatisP(AorB)?
A) 0.4 B) 0 C) 0.03 D) 0.2
5) GiventhatP(AorB)=1
3,P(A)=1
4,andP(AandB)=1
8,findP(B).
A) 5
24 B) 5
32 C) 17
24 D) 11
24
Page78
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
6) Usethefollowinggraph,whichshowsthetypesofincidentsencounteredwithdriversusingcellphones,to
findtheprobabilitythatarandomlychosenincidentinvolveseitherswervingoralmosthittingacar.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
7) Thetableliststhesmokinghabitsofagroupofcollegestudents.
Sex Non–smoker RegularSmoker HeavySmoker Total
Man 135 36 5 176
Woman 187 21 15 223
Total 322 57 20 399

Ifastudentischosenatrandom,findtheprobabilityofgettingsomeonewhoisaregularorheavysmoker.
Roundyouranswertothreedecimalplaces.
A) 0.193 B) 0.662 C) 0.221 D) 0.128
8) Thetableliststhesmokinghabitsofagroupofcollegestudents.
Sex Non–smoker RegularSmoker HeavySmoker Total
Man 135 34 5 174
Woman 187 21 10 218
Total 322 55 15 392

Ifastudentischosenatrandom,findtheprobabilityofgettingsomeonewhoisamanoranon –smoker.
Roundyouranswertothreedecimalplaces.
A) 0.921 B) 0.945 C) 0.941 D) 0.860
9) Thetableliststhesmokinghabitsofagroupofcollegestudents.
Sex Non–smoker RegularSmoker HeavySmoker Total
Man 135 42 5 182
Woman 187 21 10 218
Total 322 63 15 400
Ifastudentischosenatrandom,findtheprobabilityofgettingsomeonewhoisamanorawoman.Round
youranswertothreedecimalplaces.
A) 1 B) 0.923 C) 0.805 D) 0.195
Page79
10) ThedistributionofMasterʹsdegreesconferredbyauniversityislistedinthetable.
Assumethatastudentmajorsinonlyonesubject.
Major Frequency
Mathematics 224
English 200
Engineering 86
Business 176
Education 222

WhatistheprobabilitythatarandomlyselectedstudentwithaMasterʹsdegreemajoredinEnglishor
Mathematics?Roundyouranswertothreedecimalplaces.
A) 0.467 B) 0.533 C) 0.247 D) 0.220
11) Onehundredpeoplewereasked,ʺDoyoufavorthedeathpenalty?ʺOfthe33thatansweredʺyesʺtothe
question,14weremale.Ofthe67thatansweredʺnoʺtothequestion,sixweremale.Ifonepersonisselectedat
random,whatistheprobabilitythatthispersonansweredʺyesʺorwasamale?
A) 0.39 B) 0.53 C) 0.67 D) 0.13
3 UsetheAdditionRuleforThreeEvents
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Usethepiechart,whichshowsthenumberofCongressionalMedalofHonorrecipients,tofindtheprobability
thatarandomlychosenrecipientservedintheArmy,Navy,orMarines.
Page80
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) ThedistributionofMasterʹsdegreesconferredbyauniversityislistedinthetable.
Assumethatastudentmajorsinonlyonesubject.
Major Frequency
Mathematics 216
English 207
Engineering 84
Business 171
Education 226

WhatistheprobabilitythatarandomlyselectedstudentwithaMasterʹsdegreemajoredinBusiness,Education
orEngineering?Roundyouranswertothreedecimalplaces.
A) 0.532 B) 0.468 C) 0.282 D) 0.343
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
3) IntheVenndiagrambelow,eventArepresentstheadultswhodrinkcoffee,eventBrepresentstheadultswho
drinktea,andeventCrepresentstheadultswhodrinkcola.Listtheregion(s)whichrepresenttheadultswho
drinkbothcoffeeandtea.
Page81
4) IntheVenndiagrambelow,eventArepresentstheadultswhodrinkcoffee,eventBrepresentstheadultswho
drinktea,andeventCrepresentstheadultswhodrinkcola.Listtheregion(s)whichrepresenttheadultswho
drinkonlycola.
4 Concepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) TheeventsAandBaremutuallyexclusive.IfP(A)=0.3 andP(B)=0.6
,
whatisP(AandB)?
A) 0 B) 0.18 C) 0.5 D) 0.9
3.4 AdditionalTopicsinProbabilityandCountin
g
1 PerformCalculationswithPermutations/Combinations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Performtheindicatedcalculation.
1) 6 P4
A) 360 B) 30 C) 24 D) 2
2) 10P5
A) 30,240 B) 252 C) 2 D) 5
3) 10P3
A) 720 B) 120 C) 27 D) 7
4) 9C3
A) 84 B) 168 C) 3 D) 720
5) 5P4
10P3
A) 0.17 B) 0.042 C) 0.0000083 D) 0.18
Page82
6) 5C2
9C3
A) 0.12 B) 0.040 C) 0.00099 D) 19,000
2 DistinguishPermutationsfromCombinations
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Decideifthesituationinvolvespermutations,combinations,orneither.Explainyourreasoning.
1) Thenumberofways6friendscanbeseatedinarowatamovietheater
2) Thenumberofwaysajuryof12canbeselectedfromapoolof20
3) Thenumberof5–digitpincodesifnodigitcanberepeated
4) Thenumberofwaysyoucanchoose4booksfromaselectionof8tobringonvacation
5) Thenumberofwaysinwhich5contestantsinasingingcompetitioncanfinish
6) ThenumberofwaysanairlinecanhireaflightattendantforitsEuropeanflights,aflightattendantforits
domesticflights,andaflightattendantforitsAsianflightfromapoolof35applicants
7) Thenumberoffive–letterpasswordsthatcanbecreatedwhenletterscanberepeated
3UseCountingPrinciples
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Theaccesscodetoahouseʹssecuritysystemconsistsofsix digits.Howmanydifferentcodesareavailableif
eachdigitcanberepeated?
A) 1,000,000 B) 46,656 C) 64 D) 6
2) Adeliveryroutemustincludestopsateight cities.Howmanydifferentroutesarepossible?
A) 40,320 B) 8 C) 256 D) 16,777,216
3) AtouristinIrelandwantstovisitsixdifferentcities.Howmanydifferentroutesarepossible?
A) 720 B) 120 C) 36 D) 46,656
4) Eightguestsareinvitedfordinner.Howmanywayscantheybeseatedatadinnertableifthetableisstraight
withseatsonlyononeside?
A) 40,320 B) 362,880 C) 5040 D) 1
5) TheEnvironmentalProtectionAgencymustvisitninefactoriesforcomplaintsofairpollution.Inhowmany
differentwayscanarepresentativevisitfiveofthesetoinvestigatethisweek?
A) 15,120 B) 362,880 C) 5 D) 126
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
6) Howmanywayscanajuryoffourmenandthree womenbeselectedfromtwelvemenandtenwomen?
7) HowmanywayscantwoRepublicans,oneDemocrat,andoneIndependentbechosenfromnineRepublicans,
fiveDemocrats,andtwoIndependentstofillfourpositionsoncitycouncil?
Page83
8) HowmanydifferentpermutationsofthelettersinthewordPROBABILITYarethere?
9) HowmanydifferentpermutationsofthelettersinthewordSTATISTICSarethere?
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
10) Ifacoupleplanstohaveelevenchildren,howmanygendersequencesarepossible?
A) 2048 B) 11 C) 2.853116706e+11 D) 121
11) Ifacouplehassixboysandsixgirls,howmanygendersequencesarepossible?
A) 924 B) 12 C) 8 D) 16
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
12) Astudentmustanswersevenquestionsonanexamthatcontainstwelve questions.
a)Howmanywayscanthestudentdothis?
b)Howmanywaysarethereifthestudentmustanswerthefirstandlastquestion?
13) Howmanyversionsofatestarerequiredtocoverallpossiblequestionarrangementsifthereareseven
open–endedquestionsonthetest?
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
14) Howmanywayscanfivepeople,A,B,C,D,andE,sitinarowatamovietheaterifAandBmustsittogether?
A) 48 B) 120 C) 12 D) 24
15) Howmanywayscanfivepeople,A,B,C,D,andE,sitinarowatamovietheaterifCmustsittotherightof
butnotnecessarilynexttoB?
A) 60 B) 24 C) 20 D) 48
16) Howmanywayscanfivepeople,A,B,C,D,andE,sitinarowatamovietheaterifDandEwillnotsitnextto
eachother?
A) 72 B) 24 C) 48 D) 60
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
17) Theaccesscodetoahouseʹssecuritysystemconsistsoffivedigits.Howmanydifferentcodesareavailableif
thefirstdigitcannotbezeroandthearrangementoffivefivesisexcluded?
18) InCalifornia,eachautomobilelicenseplateconsistsofasingledigitfollowedbythreeletters,followedbythree
digits.Howmanydistinctlicenseplatescanbeformediftherearenorestrictionsonthedigitsorletters?
19) InCalifornia,eachautomobilelicenseplateconsistsofasingledigitfollowedbythreeletters,followedbythree
digits.Howmanydistinctlicenseplatescanbeformedifthefirstnumbercannotbezeroandthethreeletters
cannotformʺGODʺ?
4UseCountingPrinciplestoFindProbabilities
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Acertaincodeisasequenceof7digits.Whatistheprobabilityofgenerating7 digitsandgettingthecode
consistingof1,2,...,7ifeachdigitcanberepeated?
Page84
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) Adeliveryroutemustincludestopsatfive cities.Iftherouteisrandomlyselected,findtheprobabilitythatthe
citieswillbearrangedinalphabeticalorder.Roundyouranswertofivedecimalplaces.
A) 0.00833 B) 0.00032 C) 0.03125 D) 0.20000
3) AtouristinIrelandwantstovisitseven differentcities.Iftherouteisrandomlyselected,whatistheprobability
thatthetouristwillvisitthecitiesinalphabeticalorder?Roundyouranswertofivedecimalplaces.
A) 0.00020 B) 0.00139 C) 0.00781 D) 0.14286
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
4) IntheCaliforniaStatelottery,youmustselectsixnumbersfromfifty–twonumberstowinthebigprize.The
numbersdonothavetobeinaparticularorder.Whatistheprobabilitythatyouwillwinthebigprizeifyou
buyoneticket?
Page85
Ch.3 Probability
AnswerKey
3.1 BasicConceptsofProbabilityandCounting
1 FindProbabilities
2 IdentifytheSampleSpace
Page86
3 IdentifySimpleEvents
4 UseFundamentalCountingPrinciple
5 ClassifyTypesofProbability
6 DetermineOdds
7 Concepts
3.2 ConditionalProbabilityandtheMultiplicationRule
1 DetermineBetweenIndependentandDependentEvents
2 FindConditionalProbabilities
3 UsetheMultiplicationRuletoFindProbabilities
Page87
4 UseBayesʹsTheorem
3.3 TheAdditionRule
1 DetermineifEventsAreMutuallyExclusive
2 UsetheAdditionRuletoFindProbabilities
3 UsetheAdditionRuleforThreeEvents
4 Concepts
3.4 AdditionalTopicsinProbabilityandCountin
g
1 PerformCalculationswithPermutations/Combinations
Page88
2 DistinguishPermutationsfromCombinations
3 UseCountingPrinciples
Page89