Name_______________________________________________________Date__________________CCALG2 ProbabilityReview#2

1) Whenacarisbroughttoarepairshopforaservice,theprobabilitythatitwillneedthetransmissionfluidreplacedis0.38,theprobabilitythatitwillneedthebrakepadsreplacedis0.28,andtheprobabilitythatitwillneedboththetransmissionfluidandthebrakepadsreplacedis0.16.Lettheeventthatacarneedsthetransmissionfluidreplacedbe𝑇andtheeventthatacarneedsthebrakepadsreplacedbe𝐵.

a. Usetheadditionruletofindtheprobabilitythatarandomlyselectedcarneedsthetransmissionfluidorthebrakepadsreplaced.

2) JosiewillsoonbetakingexamsinmathandSpanish.Sheestimatesthattheprobabilityshepassesthemathexamis0.9,andtheprobabilitythatshepassestheSpanishexamis0.8.Sheisalsowillingtoassumethattheresultsofthetwoexamsareindependentofeachother.

a. UsingJosie’sassumptionofindependence,calculatetheprobabilitythatshepassesbothexams.

b. FindtheprobabilitythatJosiepassesatleastoneoftheexams.(Hint:PassingatleastoneoftheexamsispassingmathorpassingSpanish.)

3) Asetof40cardsconsistsofthefollowing:

! 10 blackcardsshowingsquares! 10 blackcardsshowingcircles! 10 redcardsshowingX’s! 10redcardsshowingdiamonds

Acardwillbeselectedatrandomfromtheset.Findtheprobabilitythatthecardisblackorshowsadiamond.

4) Anumbercubehasfacesnumbered1through6,andacoinhastwosides,headsandtails.Thenumbercubewillberolledonce,andthecoinwillbeflippedonce.Findtheprobabilitiesofthefollowingevents.(Expressyouranswersasfractionsinlowestterms.)

a. Thenumbercubeshowsa6.

b. Thecoinshowsheads.

c. Thenumbercubeshowsa6,andthecoinshowsheads.

d. Thenumbercubeshowsa6,orthecoinshowsheads.

Name_______________________________________________________Date__________________CCALG2 ProbabilityReview#2

5) Thediagramaboveshowstwospinners.Forthefirstspinner,thescores1,2,and3 areequallylikely,andforthesecondspinner,thescores1,2,3,and4areequallylikely.Bothpointerswillbespun.Writingyouranswersasfractionsinlowestterms,findtheprobabilityofeachevent.

a. Thetotalofthescoresonthetwospinnersis2.

a. Thetotalofthescoresonthetwospinnersis3.

b. Thetotalofthescoresonthetwospinnersis5.

c. Thetotalofthescoresonthetwospinnersisnot5.

6) Ofthelightbulbsavailableatastore,42%arefluorescent,23%arelabeledaslonglife,and12%arefluorescentandlonglife.

a. Alightbulbwillbeselectedatrandomfromthelightbulbsatthisstore.Roundingyouranswertothenearestthousandthwherenecessary,findtheprobabilitythat

i. Theselectedlightbulbisnotfluorescent.

ii. Theselectedlightbulbisfluorescentgiventhatitislabeledaslonglife.

b. Aretheevents“fluorescent”and“longlife”independent?Explain.

Name_______________________________________________________Date__________________CCALG2 ProbabilityReview#2

7) Acreditcardcompanystatesthat42%ofitscustomersareclassifiedaslong-termcardholders,35%paytheirbillsinfulleachmonth,and23%arelong-termcardholderswhoalsopaytheirbillsinfulleachmonth.Lettheeventthatarandomlyselectedcustomerisalong-termcardholderbe𝐿andtheeventthatarandomlyselectedcustomerpayshisbillinfulleachmonthbe𝐹.

a. Whatarethevaluesof𝑃(𝐿),𝑃(𝐹),and𝑃(𝐿 and 𝐹)?

b. DrawaVenndiagram,andlabelitwiththeprobabilitiesfrompart(a).

c. Usetheconditionalprobabilityformulatocalculate𝑃(𝐿 given 𝐹).(Roundyouranswertothenearestthousandth.)

d. Usetheconditionalprobabilityformulatocalculate𝑃(𝐹 given 𝐿).(Roundyouranswertothenearestthousandth.)

e. Whichisgreater,𝑃(𝐹 given 𝐿)or𝑃(𝐹)?Explainwhythisisrelevant.

f. Rememberthattwoevents 𝐴and𝐵aresaidtobeindependentif𝑃(𝐴 given 𝐵) = 𝑃(𝐴).Aretheevents𝐹 and𝐿 independent?Explain.

Name_______________________________________________________Date__________________CCALG2 ProbabilityReview#2

8) Giventhehypothetical1000two-waytable:

PlantoVacationinNewYork

WithintheNextYear

DoNotPlantoVacationinNewYorkWithintheNext

YearTotal

WatchedtheOnlineAd 𝟑𝟎𝟎 𝟒𝟓𝟎 𝟕𝟓𝟎 DidNotWatchtheOnlineAd 𝟏𝟎𝟎 𝟏𝟓𝟎 𝟐𝟓𝟎

Total 𝟒𝟎𝟎 𝟔𝟎𝟎 𝟏,𝟎𝟎𝟎

Aretheevents“arandomlyselectedpersonwatchedtheonlinead”and“arandomlyselectedpersonplanstovacationinNewYorkwithinthenextyear”independentornotindependent?Justifyyouranswerusingprobabilitiescalculatedfrominformationinthetable.

9) ObedienceSchoolforDogsisasmallfranchisethatoffersobedienceclassesfordogs.Somepeoplethinkthatlargerdogsareeasiertotrainand,therefore,shouldnotbechargedasmuchfortheclasses.Toinvestigatethisclaim,dogsenrolledintheclasseswereclassifiedaslarge(30poundsormore)orsmall(under30pounds).Thedogswerealsoclassifiedbywhetherornottheypassedtheobedienceclassofferedbythefranchise.45%ofthedogsinvolvedintheclasseswerelarge.60%ofthedogspassedtheclass.Recordsindicatethat40%ofthedogsintheclassesweresmallandpassedthecourse.

a. Completethefollowinghypothetical1000two-waytable:

PassedtheCourse(P)

DidNotPasstheCourse(N)

Total

LargeDogs(L)

SmallDogs(S)

Total

b. FindtheP(S).

c. FindtheP(LandN).

d. FindtheP(SorP).

e. FindtheP(N|S).

f. AretheeventsNandSindependent?Explain.