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Chapter04-IntroductiontoProbability

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1.

Eachindividualoutcomeofanexperimentiscalled

a.

thesamplespace.

b.

asamplepoint.

c.

atrial.

d.

anevent.

ANSWER:

b

2.

Thecollectionofallpossiblesamplepointsinanexperimentis

a.

thesamplespace.

b.

anevent.

c.

acombination.

d.

thepopulation.

ANSWER:

a

3.

Agraphicalmethodofrepresentingthesamplepointsofanexperimentisa

a.

stackedbarchart.

b.

dotplot.

c.

stem-and-leafdisplay.

d.

treediagram.

ANSWER:

d

4.

Anexperimentconsistsofselectingastudentbodypresidentandvicepresident.Allundergraduatestudents(freshmenthroughseniors)areeligiblefortheseoffices.Howmanysamplepoints(possibleoutcomesastotheclassifications)exist?

a.

4

b.

16

c.

8

d.

32

ANSWER:

b

5.

Anyprocessthatgenerateswell-definedoutcomesisa(n)

a.

event.

b.

experiment.

c.

samplepoint.

d.

samplespace.

ANSWER:

b

6.

Thesamplespacerefersto

a.

anyparticularexperimentaloutcome.

b.

thesamplesizeminusone.

c.

thesetofallpossibleexperimentaloutcomes.

d.

anevent.

ANSWER:

c

7.

Instatisticalexperiments,eachtimetheexperimentisrepeated

a.

thesameoutcomemustoccur.

b.

thesameoutcomecannotoccuragain.

c.

adifferentoutcomemightoccur.

d.

adifferentoutcomemustoccur.

ANSWER:

c

8.

Whentheassumptionofequallylikelyoutcomesisusedtoassignprobabilityvalues,themethodusedtoassignprobabilitiesisreferredtoasthe_____method.

a.

relativefrequency

b.

subjective

c.

probability

d.

classical

ANSWER:

d

9.

ThecountingrulethatisusedforcountingthenumberofexperimentaloutcomeswhennobjectsareselectedfromasetofNobjectswhereorderofselectionisnotimportantiscalledtherulefor

a.

permutations.

b.

combinations.

c.

independentevents.

d.

multiple-stepexperiments.

ANSWER:

b

10.

ThecountingrulethatisusedforcountingthenumberofexperimentaloutcomeswhennobjectsareselectedfromasetofNobjectswhereorderofselectionisimportantiscalledthecountingrulefor

a.

permutations.

b.

combinations.

c.

independentevents.

d.

multiple-steprandomexperiments.

ANSWER:

a

11.

Fromagroupofsixpeople,twoindividualsaretobeselectedatrandom.Howmany

selectionsarepossible?

a.

12

b.

36

c.

15

d.

8

ANSWER:

c

12.

Whentheresultsofexperimentationorhistoricaldataareusedtoassignprobabilityvalues,themethodusedtoassignprobabilitiesisreferredtoasthe_____method.

a.

relativefrequency

b.

subjective

c.

classical

d.

posterior

ANSWER:

a

13.

Amethodofassigningprobabilitiesbaseduponjudgmentisreferredtoasthe_____

method.

a.

relative

b.

probability

c.

classical

d.

subjective

ANSWER:

d

14.

Theintersectionoftwomutuallyexclusiveevents

a.

canbeanyvaluebetween0to1.

b.

mustalwaysbeequalto1.

c.

mustalwaysbeequalto0.

d.

canbeanypositivevalue.

ANSWER:

c

15.

Twoeventsaremutuallyexclusive

a.

iftheirintersectionis1.

b.

iftheyhavenosamplepointsincommon.

c.

iftheirintersectionis0.5.

d.

ifmostoftheirsamplepointsareincommon.

ANSWER:

b

16.

Therangeofprobabilityvaluesis

a.

0toinfinity.

b.

minusinfinitytoplusinfinity.

c.

0to1.

d.

-1to1.

ANSWER:

c

17.

Whichofthefollowingstatementsisalwaystrue?

a.

-1P(Ei)1

b.

P(A)=1-P(Ac)

c.

P(A)+P(B)=1

d.

∑P1

ANSWER:

b

18.

Eventsthathavenosamplepointsincommonare

a.

independentevents.

b.

supplements.

c.

mutuallyexclusiveevents.

d.

complements.

ANSWER:

c

19.

Initialestimatesoftheprobabilitiesofeventsareknownas_____probabilities.

a.

subjective

b.

posterior

c.

conditional

d.

prior

ANSWER:

d

20.

Twoeventswithnonzeroprobabilities

a.

canbebothmutuallyexclusiveandindependent.

b.

cannotbebothmutuallyexclusiveandindependent.

c.

arealwaysmutuallyexclusive.

d.

arealwaysindependent.

ANSWER:

b

21.

Theadditionlawispotentiallyhelpfulwhenweareinterestedincomputingtheprobabilityof

a.

independentevents

b.

theintersectionoftwoevents

c.

theunionoftwoevents

d.

conditionalevents

ANSWER:

c

22.

Thesumoftheprobabilitiesoftwocomplementaryeventsis

a.

0.

b.

0.5.

c.

0.57.

d.

1.0.

ANSWER:

d

23.

Thesetofallpossibleoutcomesofanexperimentis

a.

asamplepoint.

b.

anevent.

c.

thepopulation.

d.

thesamplespace.

ANSWER:

d

24.

Assumingthateachofthe52cardsinanordinarydeckhasaprobabilityof1/52ofbeingdrawn,whatistheprobabilityofdrawingablackcard?

a.

1/52

b.

4/52

c.

13/52

d.

26/52

ANSWER:

b

25.

Ifasixsideddieistossedtwotimesand"3"showsupbothtimes,theprobabilityof"3"onthethirdtrialis

a.

muchlargerthananyotheroutcome.

b.

muchsmallerthananyotheroutcome.

c.

thesameasanyotheroutcome.

d.

notabletobedeterminedbeforethedieistossed.

ANSWER:

c

26.

IfAandBareindependenteventswithP(A)=0.5andP(A

∩

B)=0.12,then,P(B)=

a.

0.240.

b.

0.060.

c.

0.380.

d.

0.620.

ANSWER:

a

27.

IfP(A)=0.4,P(B|A)=0.35,P(A∪B)=0.69,thenP(B)=

a.

0.14.

b.

0.43.

c.

0.75.

d.

0.59.

ANSWER:

b

28.

Ofsixletters(A,B,C,D,E,andF),twolettersaretobeselectedatrandom.Howmanyoutcomesarepossible?

a.

30

b.

11

c.

6!

d.

15

ANSWER:

d

29.

Fourapplicationsforadmissiontoalocaluniversityarechecked,anditisdeterminedwhethereachapplicantismaleorfemale.Thenumberofsamplepointsinthisexperimentis

a.

2.

b.

4.

c.

16.

d.

8.

ANSWER:

c

30.

Assumeyourfavoritesoccerteamhas4gameslefttofinishtheseason.Theoutcomeofeachgamecanbewin,loseortie.Thenumberofpossibleoutcomesis

a.

4.

b.

12.

c.

64.

d.

81.

ANSWER:

d

31.

Eachcustomerenteringadepartmentstorewilleitherbuyornotbuysomemerchandise.Anexperimentconsistsoffollowing5customersanddeterminingwhetherornottheypurchaseanymerchandise.Thenumberofsamplepointsinthisexperimentis

a.

5.

b.

10.

c.

25.

d.

64.

ANSWER:

d

32.

Anexperimentconsistsoftossing4coinssuccessively.Thenumberofsamplepointsinthisexperimentis

a.

16.

b.

8.

c.

4.

d.

2.

ANSWER:

a

33.

Anexperimentconsistsofthreesteps.Therearefivepossibleresultsonthefirststep,twopossibleresultsonthesecondstep,andthreepossibleresultsonthethirdstep.Thetotalnumberofexperimentaloutcomesis

a.

10.

b.

625.

c.

150.

d.

180.

ANSWER:

c

34.

Iftwoeventsareindependent,then

a.

theymustbemutuallyexclusive.

b.

thesumoftheirprobabilitiesmustbeequaltoone.

c.

theirintersectionmustbezero.

d.

theproductoftheirprobabilitiesgivestheirintersection.

ANSWER:

d

35.

Bayes'theoremisusedtocompute

a.

thepriorprobabilities.

b.

theunionofevents.

c.

intersectionofevents.

d.

theposteriorprobabilities.

ANSWER:

d

36.

Thesymbol∩showsthe

a.

unionofevents.

b.

intersectionoftwoevents.

c.

sumoftheprobabilitiesofevents.

d.

samplespace.

ANSWER:

b

37.

Thesymbol∪showsthe

a.

unionofevents.

b.

intersectionoftwoevents.

c.

sumoftheprobabilitiesofevents.

d.

samplespace.

ANSWER:

a

38.

Themultiplicationlawispotentiallyhelpfulwhenweareinterestedincomputingtheprobabilityof

a.

mutuallyexclusiveevents.

b.

theintersectionoftwoevents.

c.

theunionoftwoevents.

d.

conditionalevents.

ANSWER:

b

39.

TheunionofeventsAandBistheeventcontainingallthesamplepointsbelongingto

a.

BorA.

b.

AorB.

c.

AorBorboth.

d.

AorB,butnotboth.

ANSWER:

c

40.

Ifapennyistossedthreetimesandcomesupheadsallthreetimes,theprobabilityofheadsonthefourthtrialis

a.

0.

b.

1/16.

c.

1/2.

d.

largerthantheprobabilityoftails.

ANSWER:

c

41.

Ifacoinistossedthreetimes,thelikelihoodofobtainingthreeheadsinarowis

a.

0.0.

b.

0.500.

c.

0.875.

d.

0.125.

ANSWER:

d

42.

IfAandBareindependenteventswithP(A)=0.5andP(B)=0.5,thenP(A∩B)is

a.

0.00.

b.

1.00.

c.

0.5.

d.

0.25.

ANSWER:

d

43.

IfAandBareindependenteventswithP(A)=0.4andP(B)=0.25,thenP(A∩B)=

a.

0.65.

b.

0.1.

c.

0.625.

d.

0.15.

ANSWER:

b

44.

IfAandBareindependenteventswithP(A)=0.2andP(B)=0.6,thenP(A∪B)=

a.

0.62.

b.

0.12.

c.

0.60.

d.

0.68.

ANSWER:

d

45.

IfAandBareindependenteventswithP(A)=0.05andP(B)=0.65,thenP(A∩B)=

a.

0.05.

b.

0.0325.

c.

0.65.

d.

0.8.

ANSWER:

b

46.

IfAandBaremutuallyexclusiveeventswithP(A)=0.3andP(B)=0.5,thenP(A∩B)=

a.

0.30.

b.

0.15.

c.

0.00.

d.

0.20.

ANSWER:

c

47.

IfAandBaremutuallyexclusiveeventswithP(A)=0.25andP(B)=0.4,thenP(A∪B)=

a.

0.

b.

0.15.

c.

0.1.

d.

0.65.

ANSWER:

d

48.

Alotteryisconductedusingfoururns.Eachurncontainschipsnumberedfrom0to9.Onechipisselectedatrandomfromeachurn.Thetotalnumberofsamplepointsinthesamplespaceis

a.

40.

b.

6,561.

c.

1,048,576.

d.

10,000.

ANSWER:

d

49.

Ofthelast100customersenteringacomputershop,40havepurchasedacomputer.Iftheclassicalmethodforcomputingprobabilityisused,theprobabilitythatthenextcustomerwillpurchaseacomputeris

a.

0.40.

b.

0.50.

c.

1.00.

d.

0.60.

ANSWER:

a

50.

EventsAandBaremutuallyexclusivewithP(C)=0.35andP(B)=0.25.Then,P(Bc)=

a.

0.62.

b.

0.50.

c.

0.75.

d.

0.60.

ANSWER:

c

51.

AnexperimentconsistsoffouroutcomeswithP(E1)=0.2,P(E2)=0.25,andP(E3)=0.05.TheprobabilityofoutcomeE4is

a.

0.500.

b.

0.0025.

c.

0.100.

d.

0.

ANSWER:

c

52.

EventsAandBaremutuallyexclusive.Whichofthefollowingstatementsisalsotrue?

a.

AandBarealsoindependent.

b.

P(A∪B)=P(A)P(B)

c.

P(A∪B)=P(A)+P(B)

d.

P(A∩B)=P(A)+P(B)

ANSWER:

c

53.

Asix-sideddieistossed4times.Theprobabilityofobservingfouronesinarowis

a.

4/6.

b.

1/6.

c.

1/4096.

d.

1/1296.

ANSWER:

d

54.

TheprobabilityoftheoccurrenceofeventAinanexperimentis1/3.Iftheexperimentisperformed2timesandeventAdidnotoccur,thenonthethirdtrialeventA

a.

mustoccur.

b.

mayoccur.

c.

couldnotoccur.

d.

hasa2/3probabilityofoccurring.

ANSWER:

b

55.

Aperfectlybalancedcoinistossed6times,andtailsappearsonallsixtosses.Then,ontheseventhtrial

a.

tailcannotappear.

b.

headhasalargerchanceofappearingthantail.

c.

tailhasabetterchanceofappearingthanhead.

d.

tailhassamechanceof

appearingasthe

head.

ANSWER:

d

56.

Inanexperiment,eventsAandBaremutuallyexclusive.IfP(A)=0.6,thentheprobabilityofB

a.

cannotbelargerthan0.4.

b.

canbeanyvaluegreaterthan0.6.

c.

canbeanyvaluebetween0to1.

d.

cannotbedeterminedwiththeinformationgiven.

ANSWER:

a

57.

Amethodofassigningprobabilitieswhichassumesthattheexperimentaloutcomesareequallylikelyisreferredtoasthe_____method.

a.

objective

b.

classical

c.

subjective

d.

experimental

ANSWER:

b

58.

Amethodofassigningprobabilitiesbasedonhistoricaldataiscalledthe_____method.

a.

classical

b.

subjective

c.

relativefrequency

d.

progressive

ANSWER:

c

59.

IfP(A)=0.58,P(B)=0.44,andP(A∩B)=0.25,thenP(A∪B)=

a.

1.02.

b.

0.77.

c.

0.11.

d.

0.39.

ANSWER:

b

60.

IfP(A)=0.62,P(B)=0.47,andP(A∪B)=0.88,thenP(A∩B)=

a.

0.2914.

b.

1.9700.

c.

0.6700.

d.

0.2100.

ANSWER:

d

61.

IfAandBareindependenteventswithP(A)=0.4andP(B)=0.25,thenP(A∪B)=

a.

0.65.

b.

0.55.

c.

0.10.

d.

0.75.

ANSWER:

b

62.

IfP(A)=0.50,P(B)=0.40andP(A∪B)=0.88,thenP(B|

A)=

a.

0.02.

b.

0.03.

c.

0.04.

d.

0.05.

ANSWER:

c

63.

IfAandBareindependenteventswithP(A)=0.38andP(B)=0.55,thenP(A|B)=

a.

0.209.

b.

0.000.

c.

0.550.

d.

0.380.

ANSWER:

d

64.

IfXandYaremutuallyexclusiveeventswithP(A)=0.295,P(B)=0.32,thenP(A|B)=

a.

0.0944.

b.

0.6150.

c.

1.0000.

d.

0.0000.

ANSWER:

d

65.

IfAandBareindependenteventswithP(A)=0.35andP(B)=0.20,then,P(A∪B)=

a.

0.07.

b.

0.62.

c.

0.55.

d.

0.48.

ANSWER:

d

66.

IfP(A)=0.7,P(B)=0.6,P(A∩B)=0,theneventsAandBare

a.

supplementaryevents.

b.

mutuallyexclusive.

c.

independentevents.

d.

complementsofeachother.

ANSWER:

b

67.

IfP(A)=0.45,P(B)=0.55,andP(A∪B)=0.78,thenP(A|B)=

a.

0.00

b.

0.45

c.

0.22

d.

0.40

ANSWER:

d

68.

IfP(A)=0.48,P(A∪B)=0.82,andP(B)=0.54,thenP(A∩B)=

a.

0.3936.

b.

0.3400.

c.

0.2000.

d.

1.0200.

ANSWER:

c

69.

SomeoftheCDsproducedbyamanufactureraredefective.Fromtheproductionline,4CDsareselectedandinspected.Howmanysamplepointsexistinthisexperiment?

a.

4

b.

8

c.

16

d.

256

ANSWER:

c

70.

Sixpuppieswereborninalitter,anditisdeterminedwhethereachpuppyismaleorfemale.Howmanysamplepointsexistintheaboveexperiment?

a.

64

b.

32

c.

16

d.

4

ANSWER:

a

71.

Assumeyourfavoritesoccerteamhas3gameslefttofinishtheseason.Theoutcomeofeachgamecanbewin,lose,ortie.Howmanypossibleoutcomesexist?

a.

7

b.

27

c.

36

d.

64

ANSWER:

b

72.

Eachcustomerenteringadepartmentstorewilleitherbuyornotbuysomemerchandise.Anexperimentconsistsoffollowing3customersanddeterminingwhetherornottheypurchaseanymerchandise.Howmanysamplepointsexistintheaboveexperiment?(Notethateachcustomeriseitherapurchaserornon-purchaser.)

a.

3

b.

6

c.

8

d.

9

ANSWER:

d

73.

Fromninecardsnumbered1through9,twocardsaredrawn.Considertheselectionandclassificationofthecardsasoddorevenasanexperiment.Howmanysamplepointsarethereforthisexperiment?

a.

2

b.

3

c.

4

d.

9

ANSWER:

c

74.

Acollegeplanstointerview7studentsforpossibleofferofgraduateassistantships.Thecollegehasthreeassistantshipsavailable.Howmanygroupsofthreecanthecollegeselect?

ANSWER:

35

75.

Astudenthastotake12morecoursesbeforehecangraduate.Ifnoneofthecoursesareprerequisitetoothers,howmanygroupsoffourcoursescanheselectforthenextsemester?

ANSWER:

495

76.

Fromamong8studentshowmanycommitteesconsistingof4studentscanbeselected?

ANSWER:

70

77.

Fromagroupoftenfinaliststoacontest,threeindividualsaretobeselectedforthefirstandsecondandthirdplaces.Determinethenumberofpossibleselections.

ANSWER:

720

78.

Twelveindividualsarecandidatesforpositionsofpresidentandvicepresidentofanorganization.Howmanypossibilitiesofselectionsexist?

ANSWER:

132

79.

AssumeyouhaveappliedfortwojobsAandB.TheprobabilitythatyougetanofferforjobAis0.23.TheprobabilityofbeingofferedjobBis0.19.Theprobabilityofgettingatleastoneofthejobsis0.38.

a.

Whatistheprobabilitythatyouwillbeofferedbothjobs?

b.

AreeventsAandBmutuallyexclusive?Whyorwhynot?Explain.

ANSWER:

a.

0.04

b.

No,becauseP(A∩B)≠0

80.

Assumeyouhaveappliedfortwoscholarships,aMeritscholarship(M)andanAthleticscholarship(A).TheprobabilitythatyoureceiveanAthleticscholarshipis0.18.Theprobabilityofreceivingbothscholarshipsis0.11.Theprobabilityofgettingatleastoneofthescholarshipsis0.3.

a.

WhatistheprobabilitythatyouwillreceiveaMeritscholarship?

b.

AreeventsAandMmutuallyexclusive?Whyorwhynot?Explain.

c.

ArethetwoeventsAandMindependent?Explainusingprobabilities.

d.

WhatistheprobabilityofreceivingtheAthleticscholarshipgiventhatyouhavebeenawardedtheMeritscholarship?

e.

WhatistheprobabilityofreceivingtheMeritscholarshipgiventhatyouhavebeenawardedtheAthleticscholarship?

ANSWER:

?

a.

0.23

b.

No,becauseP(A∩M)≠0

c.

No,becauseP(A∩M)≠P(A)P(M)

d.

0.4783

e.

0.6111

81.

Asurveyofasampleofbusinessstudentsresultedinthefollowinginformationregardingthegendersoftheindividualsandtheirselectedmajor.

SelectedMajor

Gender

Management

Marketing

Others

Total

Male

50

20

30

100

Female

30

20

50

100

Total

80

40

80

200

?

a.

WhatistheprobabilityofselectinganindividualwhoismajoringinMarketing?

b.

WhatistheprobabilityofselectinganindividualwhoismajoringinManagement,giventhatthepersonisfemale?

c.

Giventhatapersonismale,whatistheprobabilitythatheismajoringinManagement?

d.

Whatistheprobabilityofselectingamaleindividual?

ANSWER:

?

a.

0.2

b.

0.3

c.

0.5

d.

0.5

82.

SixtypercentofthestudentbodyatUTCisfromthestateofTennessee(T),30%percentarefromotherstates(O),andtheremainderareinternationalstudents(I).TwentypercentofstudentsfromTennesseeliveinthedormitories,whereas,50%ofstudentsfromotherstatesliveinthedormitories.Finally,80%oftheinternationalstudentsliveinthedormitories.

a.

WhatpercentageofUTCstudentsliveinthedormitories?

b.

Giventhatastudentlivesinthedormitory,whatistheprobabilitythatshe/heisaninternationalstudent?

c.

Giventhatastudentlivesinthedormitory,whatistheprobabilitythatshe/heisfromTennessee?

ANSWER:

a.

35%

b.

0.2286(rounded)

c.

0.3429(rounded)

83.

Theprobabilityofaneconomicdeclineintheyear2008is0.23.Thereisaprobabilityof0.64thatwewillelectarepublicanpresidentintheyear2008.Ifweelectarepublicanpresident,thereisa0.35probabilityofaneconomicdecline.LetD

representtheeventofaneconomicdecline,andR

representtheeventofelectionofaRepublicanpresident.

a.

AreR

andDindependentevents?

b.

WhatistheprobabilityofaRepublicanpresidentandeconomicdeclineintheyear2008?

c.

Ifweexperienceaneconomicdeclineintheyear2008,whatistheprobabilitythattherewillaRepublicanpresident?

d.

WhatistheprobabilityofeconomicdeclineoraRepublicanpresidentintheyear2008?Hint:YouwanttofindP(D∪R).

ANSWER:

?

a.

No,becauseP(D)≠P(D?R)

b.

0.224

c.

0.9739

d.

0.646

84.

AsacompanymanagerforClaimstatCorporationthereisa0.40probabilitythatyouwillbepromotedthisyear.Thereisa0.72probabilitythatyouwillgetapromotion,araise,orboth.Theprobabilityofgettingapromotionandaraiseis0.25.

a.

Ifyougetapromotion,whatistheprobabilitythatyouwillalsogetaraise?

b.

Whatistheprobabilitythatyouwillgetaraise?

c.

Aregettingaraiseandbeingpromotedindependentevents?Explainusingprobabilities.

d.

Arethesetwoeventsmutuallyexclusive?Explainusingprobabilities.

ANSWER:

?

a.

0.625

b.

0.57

c.

No,becauseP(R)≠P(R?P)

d.

No,becauseP(R∩P)≠0

85.

Acompanyplanstointerview10recentgraduatesforpossibleemployment.Thecompanyhasthreepositionsopen.Howmanygroupsofthreecanthecompanyselect?

ANSWER:

120

86.

Astudenthastotake7morecoursesbeforeshecangraduate.Ifnoneofthecoursesareprerequisitestoothers,howmanygroupsofthreecoursescansheselectforthenextsemester?

ANSWER:

35

87.

Howmanycommittees,consistingof3femaleand3malestudents,canbeselectedfromagroupof7femaleand8malestudents?

ANSWER:

1960

88.

Eightvitaminandsixsugartabletsidenticalinappearanceareinabox.OnetabletistakenatrandomandgiventoPersonA.AtabletisthenselectedandgiventoPersonB.Whatistheprobabilitythat

a.

PersonAwasgivenavitamintablet?

b.

PersonBwasgivenasugartabletgiventhatPersonAwasgivenavitamintablet?

c.

neitherwasgivenvitamintablets?

d.

bothweregivenvitamintablets?

e.

PersonAwasgivenasugartabletandPersonBwasgivenavitamintablet?

f.

PersonAwasgivenavitamintabletandPersonBwasgivenasugartablet?

ANSWER:

?

a.

8/14

b.

6/13

c.

15/91

d.

4/13

e.

24/91

f.

24/91

89.

Thesalesrecordsofarealestateagencyshowthefollowingsalesoverthepast200days:

Numberof

Number

HousesSold

ofDays

0

60

1

80

2

40

3

16

4

4

?

a.

Howmanysamplepointsarethere?

b.

Assignprobabilitiestothesamplepointsandshowtheirvalues.

c.

Whatistheprobabilitythattheagencywillnotsellanyhousesinagivenday?

d.

Whatistheprobabilityofsellingatleast2houses?

e.

Whatistheprobabilityofselling1or2houses?

f.

Whatistheprobabilityofsellinglessthan3houses?

ANSWER:

a.

5

b.

Numberof

HousesSold

Probability

0

0.30

1

0.40

2

0.20

3

0.08

4

0.02

c.

0.3

d.

0.3

e.

0.6

f.

0.9

90.

Abankhasthefollowingdataonthegenderandmaritalstatusof200customers.

Male

Female

Single

20

30

Married

100

50

?

a.

Whatistheprobabilityoffindingasinglefemalecustomer?

b.

Whatistheprobabilityoffindingamarriedmalecustomer?

c.

Ifacustomerisfemale,whatistheprobabilitythatsheissingle?

d.

Whatpercentageofcustomersismale?

e.

Ifacustomerismale,whatistheprobabilitythatheismarried?

f.

Aregenderandmaritalstatusmutuallyexclusive?

g.

Ismaritalstatusindependentofgender?Explainusingprobabilities.

ANSWER:

?

a.

0.15

b.

0.5

c.

0.375

d.

60%

e.

0.833

f.

No,theintersectionisnotzero.

g.

TheyarenotindependentbecauseP(male)=0.6

P(male?single)=0.4

91.

AnapplicanthasappliedforpositionsatCompanyAandCompanyB.TheprobabilityofgettinganofferfromCompanyAis0.4,andtheprobabilityofgettinganofferfromCompanyBis0.3.Assumingthatthetwojoboffersareindependentofeachother,whatistheprobabilitythat

a.

theapplicantgetsanofferfrombothcompanies?

b.

theapplicantwillgetatleastoneoffer?

c.

theapplicantwillnotbegivenanofferfromeithercompany?

d.

CompanyAdoesnotofferherajob,butCompanyBdoes?

ANSWER:

a.

0.12

b.

0.58

c.

0.42

d.

0.18

92.

Anexperimentconsistsofthrowingtwosix-sideddiceandobservingthenumberofspotsontheupperfaces.Determinetheprobabilitythat

a.

thesumofthespotsis3.

b.

eachdieshowsfourormorespots.

c.

thesumofthespotsisnot3.

d.

neitheraonenorasixappearoneachdie.

e.

apairofsixesappear.

f.

thesumofthespotsis7.

ANSWER:

a.

2/36

b.

9/36

c.

34/36

d.

16/36

e.

1/36

f.

6/36

93.

Threeofthecylindersinaneight-cylindercararedefectiveandneedtobereplaced.Iftwocylindersareselectedatrandom,whatistheprobabilitythat

a.

twodefectivecylindersareselected?

b.

nodefectivecylinderisselected?

c.

atleastonedefectivecylinderisselected?

ANSWER:

?

a.

3/32

b.

5/16

c.

11/56

94.

AssumetwoeventsAandBaremutuallyexclusiveand,furthermore,P(A)=0.5andP(B)=0.25.

a.

FindP(A∩B).

b.

FindP(A∪B).

ANSWER:

?

a.

0

b.

0.75

95.

Fortypercentofthestudentswhoenrollinastatisticscoursegotothestatisticslaboratoryonaregularbasis.Pastdataindicatesthat65%ofthosestudentswhousethelabonaregularbasismakeagradeofAinthecourse.Ontheotherhand,only15%ofstudentswhodonotgotothelabonaregularbasismakeagradeofA.IfaparticularstudentmadeanA,determinetheprobabilitythatsheorheusedthelabonaregularbasis.

ANSWER:

0.743

96.

Agovernmentagencyhas6,000employees.Theemployeeswereaskedwhethertheypreferredafour-dayworkweek(10hoursperday),afive-dayworkweek(8hoursperday),orflexiblehours.Youaregiveninformationontheemployees'responsesbrokendownbysex.

Male

Female

Total

Fourdays

300

600

900

Fivedays

1,200

1,500

2,700

Flexible

300

2,100

2,400

Total

1,800

4,200

6,000

?

a.

Whatistheprobabilitythatarandomlyselectedemployeeisamanandisinfavorofafour-dayworkweek?

b.

Whatistheprobabilitythatarandomlyselectedemployeeisfemale?

c.

Arandomlyselectedemployeeturnsouttobefemale.Computetheprobabilitythatsheisinfavorofflexiblehours.

d.

Whatpercentageofemployeesisinfavorofafive-dayworkweek?

e.

Giventhatapersonisinfavorofflexibletime,whatistheprobabilitythatthepersonisfemale?

f.

Whatpercentageofemployeesismaleandinfavorofafive-dayworkweek?

ANSWER:

a.

0.05

b.

0.7

c.

0.5

d.

45%

e.

0.875

f.

20%

97.

Acorporationhas15,000employees.Sixty-twopercentoftheemployeesaremale.Twenty-threepercentoftheemployeesearnmorethan$30,000ayear.Eighteenpercentoftheemployeesaremaleandearnmorethan$30,000ayear.

a.

Ifanemployeeistakenatrandom,whatistheprobabilitythattheemployeeismale?

b.

Ifanemployeeistakenatrandom,whatistheprobabilitythattheemployeeearnsmorethan$30,000ayear?

c.

Ifanemployeeistakenatrandom,whatistheprobabilitythattheemployeeismaleandearnsmorethan$30,000ayear?

d.

Ifanemployeeistakenatrandom,whatistheprobabilitythattheemployeeismaleorearnsmorethan$30,000ayear?

e.

Theemployeetakenatrandomturnsouttobemale.Computetheprobabilitythatheearnsmorethan$30,000ayear.

f.

Arebeingmaleandearningmorethan$30,000ayearindependent?

ANSWER:

a.

0.62

b.

0.23

c.

0.18

d.

0.67

e.

0.2903

f.

No

98.

Inthetwoupcomingbasketballgames,theprobabilitythatUTCwilldefeatMarshallis0.63,andtheprobabilitythatUTCwilldefeatFurmanis0.55.Theproba