Ch.10 CountingandProbability
10.1 Counting
1 FindAlltheSubsetsofaSet
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writedownallthesubsetsofthegivenset.
1) {1
,
3
,
6
,
10}
A) {1},{3},{6},{10},{1
,
3},{1
,
6},{1
,
10},{3
,
6},
{3,10},{6,10},{1,3,6},{1,3,10},{1,6,10},{3,6,10},{1,3,6,10},∅
B) {1},{3},{6},{10},{1
,
3},{1
,
6},{1
,
10},{3
,
6},
{3,10},{1,3,6},{1,3,10},{1,6,10},{3,6,10},
{1,3,6,10},∅
C) {1},{3},{6},{10},{1
,
3},{1
,
6},{1
,
10},{3
,
6},
{3,10},{6,10},{1,3,6},{1,3,10},{1,6,10},{3,6,10},{1,3,6,10}
D) {1},{3},{6},{10},{1
,
3},{1
,
6},{1
,
10},{3
,
6},
{3,10},{6,10},{1,3,6},{1,3,10},{1,6,10},
{3,6,10},∅
2) {1
,
α
,
7
,
π}
A) {1},{α},{7},{π},{1
,
α},{1
,
7},{1
,
π},{α
,
7},
{α,π},{7,π},{1,α,7},{1,α,π},{1,7,π},{α,7,π},
{1,α,7,π},∅
B) {1},{α},{7},{π},{1
,
α},{1
,
7},{1
,
π},{α
,
7},
{α,π},{7,π},{1,α,7},{1,α,π},{1,7,π},{α,7,π},∅
C) {1},{α},{7},{π},{1
,
α},{1
,
7},{1
,
π},{α
,
7},
{α,π},{7,π},{1,α,7},{1,α,π},{1,7,π},{α,7,π},
{1,α,7,π}
D) {1},{α},{7},{π},{1
,
α},{1
,
7},{1
,
π},{α
,
7},
{α,π},{7,π},{1,α,π},{1,7,π},{α,7,π},
{1,α,7,π},∅
3) {a}
A) ∅
,
{a} B) {a} C) {a,b} D) a
4) {p,q,r}
A) ∅
,
{p},{q},{r},{p,q},{p,r},{q,r},{p,q,r}
B) {p},{q},{r},{p,q},{p,r},{q,r},{p,q,r}
C) ∅
,
{p},{q},{r},{p,q},{p,r},{q,r}
D) ∅
,
{p},{q},{r},{p,q},{p,r},{q,r},{p,p},{q,q},{r,r},{p,q,r}
2 CounttheNumberofElementsinaSet
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Ifn(A)=26
,
n(B)=22
,
andn(A∩B)=4
,
findn(A∪B).
A) 44 B) 40 C) 48 D) 52
2) Ifn(A)=22
,
n(B)=24
,
andn(A∪B)=39
,
findn(A∩B).
A) 7 B) 32 C) 14 D) 46
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3) Ifn(B)=12
n(A∩B)=3
,
andn(A∪B)=21
,
findn(A).
A) 12 B) 10 C) 14 D) 9
4) Ifn(A)=20
n(A∪B)=58
,
andn(A∩B)=16
,
findn(B).
A) 54 B) 55 C) 53 D) 38
5) Ifn(A∪B)=62
,
n(A∩B)=30
,
andn(A)=n(B),findn(A).
A) 46 B) 16 C) 31 D) 15
Usetheinformationgiveninthefigure.
6)
3
18 4 21
14
27 12
HowmanyareinsetA?
A) 26 B) 22 C) 38 D) 18
7)
1
27 3 19
15
24 5
HowmanyareinBorC?
A) 53 B) 50 C) 48 D) 8
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8)
2
24 4 21
53
20 3
HowmanyareinBandC?
A) 7 B) 4 C) 44 D) 55
9)
4
21 5 22
54
20 5
HowmanyareinBbutnotinA?
A) 26 B) 35 C) 31 D) 22
10)
5
23 4 25
34
22 10
HowmanyarenotinC?
A) 63 B) 53 C) 64 D) 58
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11)
2
22 1 20
45
16 10
HowmanyareinAandBandC?
A) 1 B) 12 C) 58 D) 70
12)
2
23 5 16
35
15 9
HowmanyareinAorBorC?
A) 69 B) 78 C) 5 D) 15
Solvetheproblem.
13) Inasurveyof55hospitalpatients,25 saidtheyweresatisfiedwiththenursingcare,20saidtheywere
satisfiedwiththemedicaltreatment,and6saidtheyweresatisfiedwithboth.Howmanypatientswere
satisfiedwithneither?Howmanyweresatisfiedwithonlythemedicaltreatment?
A) 16;14 B) 22;20 C) 16;20 D) 19;14
14) Inasurveyof392computerbuyers,164 putpriceasamainconsideration,232putperformanceasamain
consideration,and60listedbothpriceandperformance.Howmanycomputerbuyerslistedother
considerations?Howmanylookedonlyforperformance?
A) 56;172 B) 116;232 C) 56;232 D) 104;172
15) Insurveyof50households,25respondedthattheyhaveanHDTVtelevision,35respondedthattheyhad
amultimediapersonalcomputerand15respondedtheyhadboth.Howmanyhouseholdshadneitheran
HDTVtelevisionnoramultimediapersonalcomputer?
A) 5 B) 35 C) 15 D) 25
16) Inastudentsurvey,101studentsindicatedthattheyspeakSpanish,32 studentsindicatedthattheyspeak
French,10studentsindicatedthattheyspeakbothSpanishandFrench,and123studentsindicatedthat
theyspeakneither.Howmanystudentsparticipatedinthesurvey?
A) 246 B) 256 C) 236 D) 123
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17) Amongagroupof67investors,19ownedsharesofStockA,25 ownedsharesofStockB,42 ownedshares
ofStockC,10ownedsharesofbothStockAandStockB,11ownedsharesofStockAandStockC,16
ownedsharesofStockBandStockC,and7ownedsharesofallthree.Howmanyinvestorsdidnothave
sharesinanyofthethree?HowmanyownedsharesofeitherStockAorStockCbutnotStockB?
A) 11;31 B) 18;27 C) 11;27 D) 11;34
18) Inasurveyof113vacationersinapopularbeachresorttown,58 indicatedtheywouldconsiderbuyinga
homethere,46wouldconsiderbuyingabeachvilla,43wouldconsiderbuyingalot,18wouldconsider
bothahomeandavilla,24wouldconsiderbothahomeandalot,14wouldconsiderbothavillaandalot,
and8wouldconsiderallthree.Howmanyvacationerswouldnotconsideranyofthethree?Howmany
wouldconsideronlyahome?
A) 14;24 B) 22;34 C) 14;13 D) 14;22
19) Asurveyof2481creditcardusersindicatedthat1254 hadboughtbooksonline,1141hadboughtmusic
online,417hadboughtpetsuppliesonline,124hadboughtbothbooksandmusic,217hadboughtboth
booksandpetsupplies,175hadboughtbothmusicandpetsupplies,and78hadboughtallthree.How
manycreditcardusersdidnotbuyanyofthethree?Howmanyboughteitherbooksorpetsuppliesbut
notmusic?
A) 107;1233 B) 185;1094 C) 107;1094 D) 107;1172
20) Thefollowingdatarepresentthemaritalstatusoffemales18yearsandolderinacertainU.S.city.
MaritalStatus Number(inthousands)
Married 302
Widowed 52
Divorced 60
Nevermarried 113
Determinethenumberoffemales18yearsoldandolderwhoaremarriedorwidowed.
A) 354,000 B) 302,000 C) 414,000 D) 362,000
3 SolveCountingProblemsUsingtheMultiplicationPrinciple
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Amanhas2shirtsand11ties.Howmanydifferentshirtandtiearrangementscanhewear?
A) 22 B) 4 C) 44 D) 121
2) Arestaurantoffersachoiceof4salads,7 maincourses,and2 desserts.Howmanypossible3–course
mealsarethere?
A) 56possiblemeals B) 13 possiblemeals
C) 28possiblemeals D) 112 possiblemeals
3) Lisahas5skirts,7blouses,and2jackets.Howmany3–pieceoutfitscansheputtogetherassumingany
piecegoeswithanyother?
A) 70possibleoutfits B) 14 possibleoutfits
C) 35possibleoutfits D) 140 possibleoutfits
4) Howmany10–symbolcodescanbeformedusing3 differentsymbols?Repeatedsymbolsareallowed.
A) 59,049 B) 604,800 C) 120 D) 720
Page5
5) Acertainmathematicstestconsistsof20questions.Goldiedecidestoanswerthequestionswithou
t
readingthem.InhowmanywayscanGoldiefillintheanswersheetifthepossibleanswersaretrueand
false?
A) 1,048,576 B) 400 C) 40 D) 190
6) Astudentmustchoose1of4mathematicselectives,1of7 scienceelectives,and1of4programming
electives.Howmanypossiblecourseselectionsarethere?
A) 112courseselections B) 15 courseselections
C) 28courseselections D) 224 courseselections
7) Howmanyarrangementsofanswersarepossibleinamultiple–choicetestwith10questions,eachof
whichhas4possibleanswers?
A) 1,048,576 B) 151,200 C) 210 D) 5040
8) Howmany3–lettercodescanbeformedusingthelettersA,B,C,D,E,F,G,H,andI.Repeatedlettersare
allowed.
A) 729 B) 504 C) 84 D) 19,683
9) Howmany7–digitnumberscanbeformedusingthedigits0,1,2,3,4,5,6,7,8,and9ifthefirstdigit
cannotbe0?Repeateddigitsareallowed.
A) 9,000,000 B) 181,440 C) 1,360,800 D) 4,782,969
10) Howmanydifferentlicenseplatescanbemadeusing2 lettersfollowedby2 digitsselectedfromthedigits
0through9,iflettersanddigitsmayberepeated?
A) 67,600 B) 4 C) 36 D) 260
10.2 PermutationsandCombinations
1 SolveCountingProblemsUsingPermutationsInvolvingnDistinctObjects
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthevalueofthepermutation.
1) P(11
,
6)
A) 332,640 B) 55,440 C) 166,320 D) 240
2) P(8
,
0)
A) 1 B) 40,320 C) 4 D) 80,640
3) P(5
,
1)
A) 5 B) 120 C) 1 D) 24
4) P(6
,
6)
A) 720 B) 1 C) 360 D) 2
Page6
Solvetheproblem.
5) Listalltheorderedarrangementsof6objectsa,b,c,d,e,andfchoosing2atatimewithoutrepetition.
WhatisP(6,2)?
A) ab,ac,ad,ae,af,ba,bc,bd,be,bf,ca,cb,cd,ce,cf,da,db,dc,de,df,ea,eb,ec,ed,ef,fa,fb,fc,fd,fe
P(6,2)=30
B) ab,ac,ad,ae,af,bc,bd,be,bf,cd,ce,cf,de,df,ef
P(6,2)=15
C) aa,ab,ac,ad,ae,af,ba,bb,bc,bd,be,bf,ca,cb,cc,cd,ce,cf,da,db,dc,dd,de,df,ea,eb,ec,ed,ee,ef,
fa,fb,fc,fd,fe,ff
P(6,2)=36
D) ab,ac,ad,ae,af,ba,bc,bd,be,bf,ca,cb,cd,ce,cf,da,db,dc,de,df,ea,eb,ec,ed,ef
P(6,2)=25
6) Listalltheorderedarrangementsof4objects1,2,3,and4choosing3atatimewithoutrepetition.Whatis
P(4,3)?
A) 123,124,132,134,142,143,213,214,231,234,241,243,312,314,321,324,341,342,412,413,421,
423,431,432
P(4,3)=24
B) 123,124,134,234
P(4,3)=4
C) 123,124,132,142,143,213,214,231,241,243,312,314,321,341,342,412,413,421,423,431
P(4,3)=20
D) 111,112,113,114,121,122,123,124,131,132,133,134,141,142,143,144,211,212,213,214,221,222,
223,224,231,232,233,234,241,242,243,244,311,312,313,314,321,322,323,324,331,332,333,334,
341,342,343,344,411,412,413,414,421,422,423,424,431,432,433,434,441,442,443,444
P(4,3)=64
7) Inhowmanywayscan9peoplebelinedup?
A) 362,880 B) 9 C) 181,440 D) 1
8) 5differentbooksaretobearrangedonashelf.Howmanydifferentarrangementsarepossible?
A) 120 B) 5 C) 60 D) 24
9) Howmanydifferent8–lettercodesarethereifonlythelettersA,B,C,D,E,F,G,H,andIcanbeusedand
nolettercanbeusedmorethanonce?
A) 362,880 B) 43,046,721 C) 9 D) 8
10) Howmany4–digitnumberscanbeformedusingthedigits1,2,3,4,5,6,7,8,9,and0?Nodigitcanbe
usedmorethanonce.
A) 5040 B) 151,200 C) 210 D) 302,400
11) Howmanydifferentlicenseplatescanbemadeusing3 lettersfollowedby2 digitsselectedfromthedigits
0through9,ifneitherlettersnordigitsmayberepeated?
A) 1,404,000 B) 1,757,600 C) 117,000 D) 1,123,200
12) Howmanydifferentlicenseplatescanbemadeusing3 lettersfollowedby3 digitsselectedfromthedigits
0through9,ifdigitsmayberepeatedbutlettersmaynotberepeated?
A) 15,600,000 B) 3095.2381 C) 12,654,720 D) 17,576,000
13) Inhowmanywayscan4peopleeachhavedifferentbirthmonths?
A) 11,880 B) 495 C) 20,736 D) 48
Page7
14) Agroupof11friendsgoesbowling.Howmanydifferentpossibilitiesaretherefortheorderinwhichthey
playiftheyoungestpersonistobowlfirst?
A) 3,628,800 B) 39,916,800 C) 10 D) 11
2 SolveCountingProblemsUsingCombinations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthevalueofthecombination.
1) C(9
,
1)
A) 9 B) 362,880 C) 4.5 D) 80,640
2) C(6
,
6)
A) 1 B) 720 C) 180 D) 0.5
Solvetheproblem.
3) Listallthecombinationsof6objectsa,b,c,d,e,andftaken2atatime.WhatisC(6,2)?
A) ab,ac,ad,ae,af,bc,bd,be,bf,cd,ce,cf,de,df,ef
C(6,2)=15
B) ab,ac,ad,ae,af,ba,bc,bd,be,bf,ca,cb,cd,ce,cf,da,db,dc,de,df,ea,eb,ec,ed,ef,fa,fb,fc,fd,fe
C(6,2)=30
C) aa,ab,ac,ad,ae,af,ba,bb,bc,bd,be,bf,ca,cb,cc,cd,ce,cf,da,db,dc,dd,de,df,ea,eb,ec,ed,ee,ef,
fa,fb,fc,fd,fe,ff
C(6,2)=36
D) ab,ac,ad,ae,bc,bd,be,cd,ce,cf,de,df
C(6,2)=12
4) Listallthecombinationsof4objects1,2,3,and4taken3atatime.WhatisC(4,3)?
A) 123,124,134,234
C(4,3)=4
B) 123,124,132,134,142,143,213,214,231,234,241,243,312,314,321,324,341,342,412,413,421,
423,431,432
C(4,3)=24
C) 123,124,134,234,321,432
C(4,3)=6
D) 111,112,113,114,121,122,123,124,131,132,133,134,141,142,143,144,211,212,213,214,221,222,
223,224,231,232,233,234,241,242,243,244,311,312,313,314,321,322,323,324,331,332,333,334,
341,342,343,344,411,412,413,414,421,422,423,424,431,432,433,434,441,442,443,444
C(4,3)=64
5) From9namesonaballot,acommitteeof3 willbeelectedtoattendapoliticalnationalconvention.Ho
w
manydifferentcommitteesarepossible?
A) 84 B) 504 C) 60,480 D) 252
6) Ahotdogstandsellshotdogswithcheese,relish,chili,tomato,onion,mustard,orketchup.Howmany
differenthotdogscanbeconcoctedusingany3oftheextras?
A) 35 B) 210 C) 840 D) 105
7) Anexamconsistsof9multiple–choicequestionsand6essayquestions.Ifthestudentmustanswer6 ofthe
multiple–choicequestionsand3oftheessayquestions,inhowmanywayscanthequestionsbechosen?
A) 1680 B) 972 C) 261,273,600 D) 7,257,600
Page8
8) Maryfinds9fishatapetstorethatshewouldliketobuy,butshecanaffordonly5ofthem.Inhowmany
wayscanshemakeherselection?Howmanywayscanshemakeherselectionifhedecidesthatoneofthe
fishisamust?
A) 126;70 B) 15,120;1680 C) 3024;1680 D) 7560;840
9) Howmany5–cardpokerhandsconsistingofthree8ʹsandtwocardsthatarenot8ʹsarepossibleina
52–carddeck?
A) 4512 B) 2256 C) 5304 D) 2652
10) Acommitteeistobeformedconsistingof5 menand3 women.Ifthecommitteemembersaretobechosen
from13menand9women,howmanydifferentcommitteesarepossible?
A) 108,108 B) 319,770 C) 77,837,760 D) 1371
11) Howmanywaysaretheretochooseasoccerteamconsistingof3forwards,4midfieldplayers,and3
defensiveplayers,iftheplayersarechosenfrom10forwards,6midfieldplayers,and5defensiveplayers?
A) 18,000 B) 352,716 C) 15,552,000 D) 145
3 SolveCountingProblemsUsingPermutationsInvolvingnNondistinctObjects
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Howmanydifferent10–letterwords(realorimaginary)canbeformedfromthelettersintheword
IMMUNOLOGY?
A) 907,200 B) 3,628,800 C) 1,814,400 D) 90,720
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
2) Howmanydifferent11–letterwords(realorimaginary)canbeformedfromthelettersoftheword
MISSISSIPPI?Leaveyouranswerinfactorialform.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
3) Howmanydifferentverticalarrangementsarethereof9 flagsif4 arewhite,3areblue,and2 are red?
A) 1260 B) 24 C) 26 D) 126
4) Anenvironmentalorganizationhas29 members.Eachmemberwillbeplacedonexactly1of4teams.
Eachteamwillworkonadifferentissue.Thefirstteamhas7members,thesecondhas8,thethirdhas10,
andthefourthhas4.Inhowmanywayscantheseteamsbeformed?
A) 4.995897112×1014 B) 8.841761994×1030
C) 3.186978563×1024 D) 1.998358845×1015
Page9
10.3 Probability
1 ConstructProbabilityModels
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Inaprobabilitymodel,whichofthefollowingnumberscouldbetheprobabilityofanoutcome:
0,0.2,–0.01,–1
3, 1
2, 5
4,1,1.5
A) 0,0.2, 1
2,1 B) 0.2, 1
2,1
C) 0,0.2,–0.01,1,1.5 D) 0,0.2,–0.01,–1
3, 1
2,1
Determinewhetherthefollowingisaprobabilitymodel.
2)
Outcome Probability
Red 0.23
Blue 0.27
Green 0.30
White 0.20
A) Yes B) No
3)
Outcome Probability
Red 0.15
Blue 0.21
Green 0.27
White 0.50
A) Yes B) No
4)
Outcome Probability
Red 0.13
Blue 0.15
Green 0.30
White 0.27
A) Yes B) No
5)
Outcome Probability
Red –0.19
Blue 0.25
Green 0.26
White 0.30
A) Yes B) No
Page10
6)
Outcome Probability
Jim 0
Tom 0
Bill 1
Carl 0
A) Yes B) No
7)
Outcome Probability
Golfing 0.10
Skiing 0.19
Swimming 0.19
Biking 0.27
Hiking 0.25
A) Yes B) No
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Constructaprobabilitymodelfortheexperiment.
8) Tossingtwofaircoinsonce
9) Tossingonefaircointhreetimes
10) Rollinga6–sidedfairdieonce
11) Rollinga6–sidedfairdieonceandtossingafaircoinonce.
12) Rollinga6–sidedfairdietwice
13) Tossingafaircointwicegiventhatthecoinisweightedsothatheadsisthreetimesaslikelyastailsto
occur.
14) SpinnerIhas4sectionsofequalarea,numbered1,2,3,and4,andSpinnerIIhas4sectionsofequalarea,
labeledRed,Yellow,Green,andBlue.SpinSpinnerIandthenspinSpinnerII.
Whatistheprobabilityofgettinga1or3followedbyRed?
15) SpinnerIhas4sectionsofequalarea,numbered1,2,3,and4.SpinnerIIhas3sectionsofequalarea,
labeledRed,Yellow,andGreen.SpinnerIIIhas2sectionsofequalarealabeledAandB.SpinSpinnerI,
thenSpinnerII,thenSpinnerIII.
Whatistheprobabilityofgettinga2,followedbyYelloworGreen,followedbyB?
16) SpinnerIhas3sectionsofequalarea,numbered1,2,and3.SpinnerIIhas3sectionsofequalarea,
labeledRed,Yellow,andGreen.SpinSpinnerItwice,thenSpinnerII.
Whatistheprobabilityofgettinga2,followedbya1,followedbyYelloworRed?
Solvetheproblem.
17) Atwelve–sideddieisweightedsothatonlythenumbers1through8 willappearandtheywilloccurwith
thesameprobability.Whatprobabilityshouldbeassignedtoeachface?
18) Adieisweightedsothataneven–numberedfaceisthreetimesaslikelytooccurasanodd–numbered
face.Whatprobabilityshouldbeassignedtoeachface?
Page11
19) Acoinisweightedsothatheadsis5timesaslikelyastailstooccur.Whatprobabilityshouldbeassigned
toheads?totails?
2 ComputeProbabilitiesofEquallyLikelyOutcomes
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Abagcontains3redmarbles,8bluemarbles,and4 greenmarbles.Ifonemarbleisselectedatrandom,
determinetheprobabilitythatitisblue.
A) 8
15 B) 1
5C) 4
15 D) 8
11
2) A6–sideddieisrolled.Whatistheprobabilityofrollinganumberlessthan6?
A) 5
6B) 5
7C) 1
6D) 1
3
3) Two6–sideddicearerolled.Whatistheprobabilitythesumofthetwonumbersonthedicewillbe6?
A) 5
36 B) 1 C) 31
36 D) 5
4) Abagcontains19ballsnumbered1through19.Whatistheprobabilityofselectingaballthathasaneven
numberwhenoneballisdrawnfromthebag?
A) 9
19 B) 19
9C) 2
19 D) 9
5) Whatistheprobabilitythatthearrowwilllandonanoddnumber?Assumethatallsectorshaveequal
area.
A) 3
5B) 2
5C) 1 D) 0
6) SupposethatthesamplespaceisS=1,2,3,4,5,6,7,8,9,10 andthatoutcomesareequallylikely.
ComputetheprobabilityoftheeventE=2,10 .
A) 1
5B) 2
9C) 2 D) 1
10
7) SupposethatthesamplespaceisS={1,2,3,4,5,6,7,8,9,10}andthatoutcomesareequallylikely.
ComputetheprobabilityoftheeventE={1,2,4,5,7,9,10}.
A) 7
10 B) 7
9C) 4
5D) 7
8) SupposethatthesamplespaceisS={1,2,3,4,5,6,7,8,9,10}andthatoutcomesareequallylikely.
ComputetheprobabilityoftheeventE:ʺanumberdivisibleby3ʺ.
A) 3
10 B) 2
5C) 1
3D) 3
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9) Findtheprobabilityofgetting2tailswhen3faircoinsaretossed.
A) 3
8B) 1
4C) 2
3D) 1
2
10) Findtheprobabilityofhaving4girlsina4–childfamily.
A) 1
16 B) 1
8C) 1
4D) 1
32
3 FindProbabilitiesoftheUnionofTwoEvents
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) GiventhatP(A)=0.56
,
P(B)=0.35
,
andP(A∩B)=0.08
,
findP(A∪B).
A) 0.83 B) 0.91 C) 0.99 D) 0.75
2) GiventhatP(A)=0.32
,
P(B)=0.53
,
andP(A∪B)=0.63
,
findP(A∩B).
A) 0.22 B) 0.41 C) 0.85 D) 0.1696
3) GiventhatP(A)=0.56andP(B)=0.33
,
findP(A∪B)ifAandBaremutuallyexclusive.
A) 0.89 B) 0.1848 C) 0 D) 0.7052
4) GiventhatP(A)=0.28andP(B)=0.61
,
findP(A∩B)ifAandBaremutuallyexclusive.
A) 0 B) 0.1708 C) 0.89 D) 0.7192
5) GiventhatP(A)=0.24
,
P(A∪B)=0.91
,
andP(A∩B)=0.10
,
findP(B).
A) 0.77 B) 0.67 C) 0.87 D) 0.14
6) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 5
$15,000–24,999 20
$25,000–34,999 26
$35,000–44,999 30
$45,000ormore 19
Whatistheprobabilitythatahouseholdhasanannualincomeof$25,000ormore?
A) 0.75 B) 0.26 C) 0.49 D) 0.51
7) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 7
$15,000–24,999 21
$25,000–34,999 26
$35,000–44,999 27
$45,000ormore 19
Whatistheprobabilitythatahouseholdhasanannualincomelessthan$25,000?
A) 0.28 B) 0.72 C) 0.21 D) 0.54
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8) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 6
$15,000–24,999 24
$25,000–34,999 26
$35,000–44,999 28
$45,000ormore 16
Whatistheprobabilitythatahouseholdhasanannualincomebetween$15,000and$44,999inclusive?
A) 0.78 B) 0.26 C) 0.52 D) 0.5
9) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.24
1 0.31
2 0.21
3 0.11
4ormore 0.13
Whatistheprobabilitythatastudenthasatleast2siblings?
A) 0.45 B) 0.24 C) 0.76 D) 0.55
10) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.26
1 0.32
2 0.19
3 0.13
4ormore 0.10
Whatistheprobabilitythatastudenthasatmost2siblings?
A) 0.77 B) 0.23 C) 0.42 D) 0.58
11) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.27
1 0.31
2 0.20
3 0.10
4ormore 0.12
Whatistheprobabilitythatastudent3ormoresiblings?
A) 0.22 B) 0.1 C) 0.12 D) 0.78
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12) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.25
1 0.33
2 0.19
3 0.14
4ormore 0.09
Whatistheprobabilitythatastudenthaslessthan2siblings?
A) 0.58 B) 0.23 C) 0.77 D) 0.19
13) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.25
1 0.33
2 0.20
3 0.10
4ormore 0.12
Whatistheprobabilitythatastudenthas1,2,or3siblings?
A) 0.63 B) 0.53 C) 0.3 D) 0.88
14) Abagcontains6redmarbles,3bluemarbles,and1 greenmarble.Whatistheprobabilityofchoosinga
marblethatisredorgreenwhenonemarbleisdrawnfromthebag?
A) 7
10 B) 10
7C) 3
10 D) 7
15) Eachoftenticketsismarkedwithadifferentnumberfrom1to10andputinabox.Ifyoudrawaticket
fromthebox,whatistheprobabilitythatyouwilldraw8,9,or5?
A) 3
10 B) 1
8C) 1
10 D) 1
9
16) Alotterygamehasballsnumbered1through17.Whatistheprobabilityofselectinganevennumbered
ballora5?
A) 9
17 B) 8
17 C) 7
17 D) 8
9
17) Aspinnerhasregionsnumbered1through15.Whatistheprobabilitythatthespinnerwillstoponan
evennumberoramultipleof3?
A) 2
3B) 7
9C) 1
3D) 12
18) Thepsychologylabatacollegeisstaffedby9 maledoctoralstudents,8 femaledoctoralstudents,16 male
undergraduates,and14femaleundergraduates.Ifapersonisselectedatrandomfromthegroup,findthe
probabilitythattheselectedpersonisanundergraduateorafemale.
A) 38
47 B) 24
47 C) 30
47 D) 22
47
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19) Thefacultyatacollegeconsistsof110 full–timeteachersand54 part–timeteachers.Ofthe110 full–time
teachers,59arefemale.Ofthe54part–timeteachers,26arefemale.Findtheprobabilitythatarandomly
selectedteacherismaleorworkspart–time.
A) 105
164 B) 133
164 C) 77
164 D) 7
41
4 UsetheComplementRuletoFindProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Abagcontains7redmarbles,3bluemarbles,and1 greenmarble.Whatistheprobabilityofchoosinga
marblethatisnotbluewhenonemarbleisdrawnfromthebag?
A) 8
11 B) 11
8C) 3
11 D) 8
2) DuringJulyinJacksonville,Florida,itisnotuncommontohaveafternoonthunderstorms.Onaverage,9.8
dayshaveafternoonthunderstorms.WhatistheprobabilitythatarandomlyselecteddayinJulywillnot
haveathunderstorm?Roundtotwodecimalplaces,ifnecessary.
A) 0.68 B) 0.67 C) 0.32 D) 0.9
3) InthecityofGloomville,theprobabilityofrainonNewYearʹsDayis44%.Whatistheprobabilitythat
nextNewYearʹsDayitwillnotraininGloomville?
A) 56% B) 44% C) –44% D) 19.36%
4) Samestimatesthatifheleaveshiscarparkedoutsidehisofficealldayonaweekday,thechancethathe
willgetaparkingticketis33%.IfSamleaveshiscarparkedoutsidehisofficealldaynextTuesday,what
isthechancethathewillnotgetaparkingticket?
A) 67% B) 33% C) –33% D) 10.89%
5) Whatistheprobabilitythatatleast2peoplehavethesamebirthmonthinagroupof6people?
A) 0.777 B) 0.223 C) 0.788 D) 0.212
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Ch.10 CountingandProbability
AnswerKey
10.1 Counting
1 FindAlltheSubsetsofaSet
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