Ch.14 CountingandProbability
14.1 Counting
1 FindAlltheSubsetsofaSet
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writedownallthesubsetsofthegivenset.
1) {3
,
5
,
10
,
11}
A) {3},{5},{10},{11},{3
,
5},{3
,
10},{3
,
11},{5
,
10},
{5,11},{10,11},{3,5,10},{3,5,11},{3,10,11},{5,10,11},{3,5,10,11},∅
B) {3},{5},{10},{11},{3
,
5},{3
,
10},{3
,
11},{5
,
10},
{5,11},{3,5,10},{3,5,11},{3,10,11},{5,10,11},
{3,5,10,11},∅
C) {3},{5},{10},{11},{3
,
5},{3
,
10},{3
,
11},{5
,
10},
{5,11},{10,11},{3,5,10},{3,5,11},{3,10,11},{5,10,11},{3,5,10,11}
D) {3},{5},{10},{11},{3
,
5},{3
,
10},{3
,
11},{5
,
10},
{5,11},{10,11},{3,5,10},{3,5,11},{3,10,11},
{5,10,11},∅
2) {4
,
α
,
8
,
π}
A) {4},{α},{8},{π},{4
,
α},{4
,
8},{4
,
π},{α
,
8},
{α,π},{8,π},{4,α,8},{4,α,π},{4,8,π},{α,8,π},
{4,α,8,π},∅
B) {4},{α},{8},{π},{4
,
α},{4
,
8},{4
,
π},{α
,
8},
{α,π},{8,π},{4,α,8},{4,α,π},{4,8,π},{α,8,π},∅
C) {4},{α},{8},{π},{4
,
α},{4
,
8},{4
,
π},{α
,
8},
{α,π},{8,π},{4,α,8},{4,α,π},{4,8,π},{α,8,π},
{4,α,8,π}
D) {4},{α},{8},{π},{4
,
α},{4
,
8},{4
,
π},{α
,
8},
{α,π},{8,π},{4,α,π},{4,8,π},{α,8,π},
{4,α,8,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)=37
,
n(B)=56
,
andn(A∩B)=18
,
findn(A∪B).
A) 75 B) 57 C) 93 D) 111
2) Ifn(A)=36
,
n(B)=22
,
andn(A∪B)=53
,
findn(A∩B).
A) 5 B) 48 C) 10 D) 58
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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)=48
,
n(A∩B)=28
,
andn(A)=n(B),findn(A).
A) 38 B) 10 C) 24 D) 14
Usetheinformationgiveninthefigure.
6)
1
30 5 16
52
21 1
HowmanyareinsetA?
A) 41 B) 36 C) 42 D) 30
7)
3
15 5 24
21
18 1
HowmanyareinBorC?
A) 53 B) 48 C) 43 D) 6
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8)
4
24 2 17
25
19 5
HowmanyareinBandC?
A) 7 B) 2 C) 41 D) 49
9)
2
30 5 16
15
17 1
HowmanyareinBbutnotinA?
A) 21 B) 28 C) 26 D) 16
10)
5
22 3 28
15
27 8
HowmanyarenotinC?
A) 63 B) 55 C) 64 D) 58
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11)
3
29 4 20
25
22 10
HowmanyareinAandBandC?
A) 4 B) 14 C) 71 D) 85
12)
4
25 1 29
34
23 3
HowmanyareinAorBorC?
A) 89 B) 92 C) 1 D) 12
Solvetheproblem.
13) Inasurveyof52hospitalpatients,22 saidtheyweresatisfiedwiththenursingcare,18saidtheywere
satisfiedwiththemedicaltreatment,and6saidtheyweresatisfiedwithboth.Howmanypatientswere
satisfiedwithneither?Howmanyweresatisfiedwithonlythemedicaltreatment?
A) 18;12 B) 24;18 C) 18;18 D) 16;12
14) Inasurveyof456computerbuyers,254 putpriceasamainconsideration,202putperformanceasamain
consideration,and56listedbothpriceandperformance.Howmanycomputerbuyerslistedother
considerations?Howmanylookedonlyforperformance?
A) 56;146 B) 112;202 C) 56;202 D) 198;146
15) Insurveyof50households,25respondedthattheyhaveanHDTVtelevision,35respondedthattheyhad
amultimediapersonalcomputerand15respondedtheyhadboth.Howmanyhouseholdshadneitheran
HDTVtelevisionnoramultimediapersonalcomputer?
A) 5 B) 35 C) 15 D) 25
16) Inastudentsurvey,121studentsindicatedthattheyspeakSpanish,31 studentsindicatedthattheyspeak
French,12studentsindicatedthattheyspeakbothSpanishandFrench,and135studentsindicatedthat
theyspeakneither.Howmanystudentsparticipatedinthesurvey?
A) 275 B) 287 C) 263 D) 140
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17) Amongagroupof70investors,27ownedsharesofStockA,31 ownedsharesofStockB,35 ownedshares
ofStockC,15ownedsharesofbothStockAandStockB,13ownedsharesofStockAandStockC,15
ownedsharesofStockBandStockC,and10ownedsharesofallthree.Howmanyinvestorsdidnothave
sharesinanyofthethree?HowmanyownedsharesofeitherStockAorStockCbutnotStockB?
A) 10;29 B) 20;26 C) 10;26 D) 10;36
18) Inasurveyof157vacationersinapopularbeachresorttown,55 indicatedtheywouldconsiderbuyinga
homethere,79wouldconsiderbuyingabeachvilla,58wouldconsiderbuyingalot,26wouldconsider
bothahomeandavilla,32wouldconsiderbothahomeandalot,27wouldconsiderbothavillaandalot,
and15wouldconsiderallthree.Howmanyvacationerswouldnotconsideranyofthethree?Howmany
wouldconsideronlyahome?
A) 35;12 B) 50;23 C) 35;14 D) 35;41
19) Asurveyof2415creditcardusersindicatedthat1097 hadboughtbooksonline,1150hadboughtmusic
online,443hadboughtpetsuppliesonline,112hadboughtbothbooksandmusic,208hadboughtboth
booksandpetsupplies,141hadboughtbothmusicandpetsupplies,and70hadboughtallthree.How
manycreditcardusersdidnotbuyanyofthethree?Howmanyboughteitherbooksorpetsuppliesbut
notmusic?
A) 116;1149 B) 186;1011 C) 116;1011 D) 116;1081
20) Thefollowingdatarepresentthemaritalstatusoffemales18yearsandolderinacertainU.S.city.
MaritalStatus Number(inthousands)
Married 307
Widowed 58
Divorced 56
Nevermarried 119
Determinethenumberoffemales18yearsoldandolderwhoaremarriedorwidowed.
A) 365,000 B) 307,000 C) 421,000 D) 363,000
3 SolveCountingProblemsUsingtheMultiplicationPrinciple
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Amanhas9shirtsand11ties.Howmanydifferentshirtandtiearrangementscanhewear?
A) 99 B) 81 C) 198 D) 121
2) Arestaurantoffersachoiceof5salads,5 maincourses,and3 desserts.Howmanypossible3–course
mealsarethere?
A) 75possiblemeals B) 13 possiblemeals
C) 25possiblemeals D) 150 possiblemeals
3) Lisahas4skirts,6blouses,and2jackets.Howmany3–pieceoutfitscansheputtogetherassumingany
piecegoeswithanyother?
A) 48possibleoutfits B) 12possibleoutfits C) 24 possibleoutfits D) 96possibleoutfits
4) Howmany8–symbolcodescanbeformedusing5 differentsymbols?Repeatedsymbolsareallowed.
A) 390,625 B) 336 C) 56 D) 6720
Page5
5) Acertainmathematicstestconsistsof20questions.Goldiedecidestoanswerthequestionswithou
t
readingthem.InhowmanywayscanGoldiefillintheanswersheetifthepossibleanswersaretrueand
false?
A) 1,048,576 B) 400 C) 40 D) 190
6) Astudentmustchoose1of5mathematicselectives,1of7 scienceelectives,and1of8programming
electives.Howmanypossiblecourseselectionsarethere?
A) 280courseselections B) 20 courseselections
C) 35courseselections D) 560 courseselections
7) Howmanyarrangementsofanswersarepossibleinamultiple–choicetestwith7questions,eachofwhich
has4possibleanswers?
A) 16,384 B) 210 C) 35 D) 840
8) Howmany5–lettercodescanbeformedusingthelettersA,B,C,D,E,F,G,H,andI.Repeatedlettersare
allowed.
A) 59,049 B) 15,120 C) 126 D) 1,953,125
9) Howmany6–digitnumberscanbeformedusingthedigits0,1,2,3,4,5,6,7,8,and9ifthefirstdigit
cannotbe0?Repeateddigitsareallowed.
A) 900,000 B) 60,480 C) 272,160 D) 531,441
10) Howmanydifferentlicenseplatescanbemadeusing2 lettersfollowedby2 digitsselectedfromthedigits
0through9,iflettersanddigitsmayberepeated?
A) 67,600 B) 4 C) 36 D) 260
14.2 PermutationsandCombinations
1 SolveCountingProblemsUsingPermutationsInvolvingnDistinctObjects
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthevalueofthepermutation.
1) P(11
,
6)
A) 332,640 B) 55,440 C) 166,320 D) 240
2) P(3
,
0)
A) 1 B) 6 C) 2 D) 12
3) P(5
,
1)
A) 5 B) 120 C) 1 D) 24
4) P(11
,
11)
A) 39,916,800 B) 1 C) 19,958,400 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) Inhowmanywayscan6peoplebelinedup?
A) 720 B) 6 C) 360 D) 1
8) 8differentbooksaretobearrangedonashelf.Howmanydifferentarrangementsarepossible?
A) 40,320 B) 8 C) 20,160 D) 5040
9) Howmanydifferent5–lettercodesarethereifonlythelettersA,B,C,D,E,F,G,H,andIcanbeusedand
nolettercanbeusedmorethanonce?
A) 15,120 B) 59,049 C) 126 D) 5
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) Howmanydifferentlicenseplatescanbemadeusing2 lettersfollowedby4 digitsselectedfromthedigits
0through9,ifneitherlettersnordigitsmayberepeated?
A) 3,276,000 B) 6,760,000 C) 68,250 D) 1,965,600
12) Howmanydifferentlicenseplatescanbemadeusing4 lettersfollowedby2 digitsselectedfromthedigits
0through9,ifdigitsmayberepeatedbutlettersmaynotberepeated?
A) 35,880,000 B) 889.880952 C) 41,127,840 D) 45,697,600
13) Inhowmanywayscan4peopleeachhavedifferentbirthmonths?
A) 11,880 B) 495 C) 20,736 D) 48
Page7
14) Agroupof12friendsgoesbowling.Howmanydifferentpossibilitiesaretherefortheorderinwhichthey
playiftheyoungestpersonistobowlfirst?
A) 39,916,800 B) 479,001,600 C) 11 D) 12
2 SolveCountingProblemsUsingCombinations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthevalueofthecombination.
1) C(11
,
5)
A) 462 B) 332,640 C) 27,720 D) 1440
2) C(8
,
8)
A) 1 B) 40,320 C) 10,080 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,acommitteeof5 willbeelectedtoattendapoliticalnationalconvention.Ho
w
manydifferentcommitteesarepossible?
A) 126 B) 15,120 C) 3024 D) 7560
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–cardpokerhandsconsistingofthree4ʹsandtwocardsthatarenot4ʹsarepossibleina
52–carddeck?
A) 4512 B) 2256 C) 5304 D) 2652
10) Acommitteeistobeformedconsistingof2 menand4 women.Ifthecommitteemembersaretobechosen
from8menand11women,howmanydifferentcommitteesarepossible?
A) 9240 B) 27,132 C) 443,520 D) 358
11) Howmanywaysaretheretochooseasoccerteamconsistingof3forwards,4midfieldplayers,and3
defensiveplayers,iftheplayersarechosenfrom8forwards,8midfieldplayers,and8defensiveplayers?
A) 219,520 B) 1,961,256 C) 189,665,280 D) 182
3 SolveCountingProblemsUsingPermutationsInvolvingnNondistinctObjects
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Howmanydifferent10–letterwords(realorimaginary)canbeformedfromthelettersintheword
MANAGEMENT?
A) 226,800 B) 3,628,800 C) 453,600 D) 22,680
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
2) Howmanydifferent11–letterwords(realorimaginary)canbeformedfromthelettersoftheword
MISSISSIPPI?Leaveyouranswerinfactorialform.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
3) Howmanydifferentverticalarrangementsarethereof7 flagsif3 arewhite,3areblue,and1 is red?
A) 140 B) 9 C) 15 D) 35
4) Anenvironmentalorganizationhas30 members.Eachmemberwillbeplacedonexactly1of4teams.
Eachteamwillworkonadifferentissue.Thefirstteamhas8members,thesecondhas6,thethirdhas7,
andthefourthhas9.Inhowmanywayscantheseteamsbeformed?
A) 4.995897112×1015 B) 2.652528598×1032
C) 1.012239098×1026 D) 4.496307401×1016
Page9
14.3 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 0.16
Blue 0.30
Green 0.32
White 0.22
A) Yes B) No
3)
Outcome Probability
Red 0.21
Blue 0.26
Green 0.31
White 0.50
A) Yes B) No
4)
Outcome Probability
Red 0.19
Blue 0.20
Green 0.27
White 0.19
A) Yes B) No
5)
Outcome Probability
Red –0.23
Blue 0.28
Green 0.31
White 0.18
A) Yes B) No
Page10
6)
Outcome Probability
Jim 0
Tom 0
Bill 1
Carl 0
A) Yes B) No
7)
Outcome Probability
Golfing 0.11
Skiing 0.22
Swimming 0.19
Biking 0.21
Hiking 0.27
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–sideddieisweightedsothatonlythenumbers1through6 willappearandtheywilloccurwith
thesameprobability.Whatprobabilityshouldbeassignedtoeachface?
18) Adieisweightedsothataneven–numberedfaceisthreetimesaslikelytooccurasanodd–numbered
face.Whatprobabilityshouldbeassignedtoeachface?
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19) Acoinisweightedsothatheadsis12 timesaslikelyastailstooccur.Whatprobabilityshouldbeassigned
toheads?totails?
2 ComputeProbabilitiesofEquallyLikelyOutcomes
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Abagcontains4redmarbles,7bluemarbles,and8 greenmarbles.Ifonemarbleisselectedatrandom,
determinetheprobabilitythatitisblue.
A) 7
19 B) 4
19 C) 8
19 D) 7
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) Abagcontains17ballsnumbered1through17.Whatistheprobabilityofselectingaballthathasaneven
numberwhenoneballisdrawnfromthebag?
A) 8
17 B) 17
8C) 2
17 D) 8
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)=0.27
,
P(B)=0.37
,
andP(A∩B)=0.05
,
findP(A∪B).
A) 0.59 B) 0.64 C) 0.69 D) 0.54
2) GiventhatP(A)=0.46
,
P(B)=0.4
,
andP(A∪B)=0.63
,
findP(A∩B).
A) 0.23 B) 0.4 C) 0.86 D) 0.184
3) GiventhatP(A)=0.23andP(B)=0.48
,
findP(A∪B)ifAandBaremutuallyexclusive.
A) 0.71 B) 0.1104 C) 0 D) 0.5996
4) GiventhatP(A)=0.59andP(B)=0.19
,
findP(A∩B)ifAandBaremutuallyexclusive.
A) 0 B) 0.1121 C) 0.78 D) 0.6679
5) GiventhatP(A)=0.54
,
P(A∪B)=0.74
,
andP(A∩B)=0.28
,
findP(B).
A) 0.48 B) 0.20 C) 0.76 D) 0.26
6) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 5
$15,000–24,999 24
$25,000–34,999 25
$35,000–44,999 28
$45,000ormore 18
Whatistheprobabilitythatahouseholdhasanannualincomeof$25,000ormore?
A) 0.71 B) 0.25 C) 0.46 D) 0.54
7) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 7
$15,000–24,999 20
$25,000–34,999 25
$35,000–44,999 25
$45,000ormore 23
Whatistheprobabilitythatahouseholdhasanannualincomelessthan$25,000?
A) 0.27 B) 0.73 C) 0.2 D) 0.52
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8) Thetablebelowshowstheresultsofaconsumersurveyofannualincomesin100households.

Income Numberofhouseholds
$0–14,999 5
$15,000–24,999 25
$25,000–34,999 29
$35,000–44,999 30
$45,000ormore 11
Whatistheprobabilitythatahouseholdhasanannualincomebetween$15,000and$44,999inclusive?
A) 0.84 B) 0.29 C) 0.55 D) 0.54
9) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.24
1 0.33
2 0.17
3 0.12
4ormore 0.14
Whatistheprobabilitythatastudenthasatleast2siblings?
A) 0.43 B) 0.26 C) 0.74 D) 0.57
10) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.23
1 0.33
2 0.20
3 0.14
4ormore 0.10
Whatistheprobabilitythatastudenthasatmost2siblings?
A) 0.76 B) 0.24 C) 0.44 D) 0.56
11) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.27
1 0.31
2 0.21
3 0.11
4ormore 0.10
Whatistheprobabilitythatastudent3ormoresiblings?
A) 0.21 B) 0.11 C) 0.1 D) 0.79
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12) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.24
1 0.31
2 0.21
3 0.12
4ormore 0.12
Whatistheprobabilitythatastudenthaslessthan2siblings?
A) 0.55 B) 0.24 C) 0.76 D) 0.21
13) Inasurveyaboutthenumberofsiblingsofcollegestudents,thefollowingprobabilitytablewas
constructed:

NumberofSiblings Probability
0 0.25
1 0.32
2 0.19
3 0.13
4ormore 0.11
Whatistheprobabilitythatastudenthas1,2,or3siblings?
A) 0.64 B) 0.51 C) 0.32 D) 0.89
14) Abagcontains6redmarbles,2bluemarbles,and1 greenmarble.Whatistheprobabilityofchoosinga
marblethatisredorgreenwhenonemarbleisdrawnfromthebag?
A) 7
9B) 9
7C) 2
9D) 7
15) Eachoftenticketsismarkedwithadifferentnumberfrom1to10andputinabox.Ifyoudrawaticket
fromthebox,whatistheprobabilitythatyouwilldraw5,8,or3?
A) 3
10 B) 1
5C) 1
10 D) 1
8
16) Alotterygamehasballsnumbered1through15.Whatistheprobabilityofselectinganevennumbered
ballora11?
A) 8
15 B) 7
15 C) 2
5D) 7
8
17) Aspinnerhasregionsnumbered1through15.Whatistheprobabilitythatthespinnerwillstoponan
evennumberoramultipleof3?
A) 2
3B) 7
9C) 1
3D) 12
18) Thepsychologylabatacollegeisstaffedby6 maledoctoralstudents,10 femaledoctoralstudents,15
maleundergraduates,and13femaleundergraduates.Ifapersonisselectedatrandomfromthegroup,
findtheprobabilitythattheselectedpersonisanundergraduateorafemale.
A) 19
22 B) 25
44 C) 7
11 D) 23
44
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19) Thefacultyatacollegeconsistsof96 full–timeteachersand50 part–timeteachers.Ofthe96 full–time
teachers,54arefemale.Ofthe50part–timeteachers,24arefemale.Findtheprobabilitythatarandomly
selectedteacherismaleorworkspart–time.
A) 46
73 B) 59
73 C) 33
73 D) 13
73
4 UsetheComplementRuletoFindProbabilities
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Solvetheproblem.
1) Abagcontains7redmarbles,4bluemarbles,and1 greenmarble.Whatistheprobabilityofchoosinga
marblethatisnotbluewhenonemarbleisdrawnfromthebag?
A) 2
3B) 3
2C) 1
3D) 8
2) DuringJulyinJacksonville,Florida,itisnotuncommontohaveafternoonthunderstorms.Onaverage,
12.1dayshaveafternoonthunderstorms.WhatistheprobabilitythatarandomlyselecteddayinJulywill
nothaveathunderstorm?Roundtotwodecimalplaces,ifnecessary.
A) 0.61 B) 0.6 C) 0.39 D) 0.88
3) InthecityofGloomville,theprobabilityofrainonNewYearʹsDayis56%.Whatistheprobabilitythat
nextNewYearʹsDayitwillnotraininGloomville?
A) 44% B) 56% C) –56% D) 31.36%
4) Samestimatesthatifheleaveshiscarparkedoutsidehisofficealldayonaweekday,thechancethathe
willgetaparkingticketis13%.IfSamleaveshiscarparkedoutsidehisofficealldaynextTuesday,what
isthechancethathewillnotgetaparkingticket?
A) 87% B) 13% C) –13% D) 1.69%
5) Whatistheprobabilitythatatleast2peoplehavethesamebirthmonthinagroupof6people?
A) 0.777 B) 0.223 C) 0.788 D) 0.212
Ch.14 CountingandProbability
AnswerKey
14.1 Counting
1 FindAlltheSubsetsofaSet
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2 SolveCountingProblemsUsingCombinations
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