working ST Core Reg - Mathematics Vision Project · SECONDARY MATH II // MODULE 9 PROBABILITY- 9.2 Mathematics Vision Project 9.2 Chocolate versus Vanilla A Solidify Understanding

The Mathematics Vision Project Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius

© 2017 Mathematics Vision Project Original work © 2013 in partnership with the Utah State Off ice of Education

This work is licensed under the Creative Commons Attribution CC BY 4.0

MODULE 9

Probability

SECONDARY

MATH TWO

An Integrated Approach

SECONDARY MATH 2 // MODULE 9

PROBABILITY

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

MODULE 9 - TABLE OF CONTENTS

PROBABILITY

9.1 TB or Not TB – A Develop Understanding Task

Estimating conditional probabilities and interpreting the meaning of a set of data (S.CP.6, S.MD.7+)

READY, SET, GO Homework: Probability 9.1

9.2 Chocolate versus Vanilla – A Solidify Understanding Task

Examining conditional probability using multiple representations (S.CP.6)


9.3 Fried Freddy’s – A Solidify Understanding Task

Using sample to estimate probabilities (S.CP.2, S.CP.6)


9.4 Visualizing with Venn – A Solidify Understanding Task

Creating Venn diagram’s using data while examining the addition rule for probability (S.CP.6, S.CP.7)


9.5 Freddy Revisited – A Solidify Understanding Task

Examining independence of events using two-way tables (S.CP.2, S.CP.3, S.CP.4, S.CP.5)


9.6 Striving for Independence – A Practice Understanding Task

Using data in various representations to determine independence (S.CP.2, S.CP.3, S.CP.4, S.CP.5)


SECONDARY MATH II // MODULE 9

PROBABILITY - 9.1


9.1 TB or Not TB? A Develop Understanding Task

Tuberculosis(TB)canbetestedinavarietyofways,includingaskintest.Ifapersonhas

turberculosisantibodies,thentheyareconsideredtohaveTB.Belowisatreediagramrepresenting

databasedon1,000peoplewhohavebeengivenaskintestforturberculosis.

1. WhatobservationsdoyounoticeaboutTBtestsbasedonthetreediagram?

2. Youmayhavenoticedthat380patientshaveTB,yetnotall380patientswithTBtestedpositive.Instatistics,thenotation:“Testednegative|TB”means‘thenumberofpatientswhotestednegative,giventhattheyhaveTB’.DeterminetheprobabilitythatapersonwhohasTBcouldreceiveanegativeresultcomparedtootherswhohaveTB.Whatdoesthismean?

Thisisanexampleofconditionalprobability,whichisthemeasureofanevent,giventhat

anothereventhasoccurred.

CCBYhttps://flic.kr/p/xXebu

Testednegative|notTB558

PatienthasT

B380

Testednegative|TB19

PatientdoesNOThaveTB620

Testedpositi

ve|TB361

Testedpositi

ve|notTB6

2

1


PROBABILITY - 9.1


3. Writeseveralotherprobabilityandconditionalprobabilitystatementsbasedonthetreediagram.

Partofunderstandingtheworldaroundusisbeingabletoanalyzedataandexplainittoothers.

4. Basedontheprobabilitystatementsfromthetreediagram,whatwouldyousaytoafriendregardingthevalidityoftheirresultsiftheyaretestingforTBusingaskintestandthe

resultcamebackpositive?

5. Inthissituation,explaintheconsequencesoferrors(havingatestwithincorrectresults).

6. Ifahealthtestisnot100%certain,whymightitbebeneficialtohavetheresultsleanmoretowardafalsepositive?

7. Isasamplespaceof200enoughtoindicatewhetherornotthisistrueforanentirepopulation?

2


PROBABILITY – 9.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

9.1

Needhelp?Visitwww.rsgsupport.org

READY

Topic:VennDiagrams,howtocreateandread.

ForeachVennDiagramprovidedanswerthequestions.

1.Howmanystudentsweresurveyed?

2.Whatwerethestudentsasked?

3.Howmanystudentsareinboth

choirandband?

4.Howmanystudentsarenotineither

choirorband?

5.Whatistheprobabilitythata

randomlyselectedstudentwouldbein

band?

ThisVennDiagramrepresentsenrollmentinsomeof

theelectivecourses.

6.Whatdoesthe95inthecentertellyou?

7.Whatdoesthe145tellyou?

8.Howmanytotalstudentsarerepresentedinthe

diagram?

9.Whichelectiveclasshastheleastnumberof

studentsenrolled?

READY, SET, GO! Name PeriodDate

3


PROBABILITY – 9.1




9.1


SET Topic:Interpretingatreediagramtodetermineprobability

Giventhetreediagrambelowanswerthequestionsanddeterminetheprobabilities.Thediagramrepresentsthenumberofplateappearancesduringthefirstmonthofaminorleaguebaseballseason.

10. Howmanytimesdidabattercometotheplateduringthistimeperiod?

11. Basedonthisdata,ifyouarealeft-handedbatterwhatistheprobabilitythatyouwillfacearight-handedpitcher?

12. Basedonthisdata,ifyouarearight-handedbatterwhatistheprobabilitythatyouwillfacealeft-handedpitcher?

13. Whatistheprobabilitythataleft-handedpitcherwillbethrowingforanygivenplateappearance?

14. Whatistheprobabilitythataleft-handedbatterwouldbeattheplateforanygivenplateappearance?

Whatobservationsdoyoumakeaboutthedata?Isthereanyamountthatseemstobeoverly

abundant?Whatmightaccountforthis?

GO Topic:BasicProbability

Findtheprobabilityofachievingsuccesswitheachoftheeventsbelow.

15. Rollinganevennumberonstandardsix-sideddie.

16. Drawingablackcardfromastandarddeckofcards.

17. FlippingacoinandgettingHeadsthreetimesinarow.

18. Rollingadieandgettingafour.

19. Drawinganacefromadeckofcards.

20. Rollingadietwiceinarowandgettingtwothrees.

21. Fromabagcontaining3blue,2red,and5whitemarbles.Pullingoutaredmarble.

4


PROBABILITY- 9.2


9.2 Chocolate versus Vanilla A Solidify Understanding Task

Danielleloveschocolateicecreammuchmorethanvanillaandwas

explainingtoherbestfriendRaquelthatsodoesmostoftheworld.Raquel

disagreedandthoughtvanillaismuchbetter.Tosettletheargument,they

createdasurveyaskingpeopletochoosetheirfavoriteicecreamflavor

betweenchocolateandvanilla.Aftercompletingthesurvey,thefollowing

resultscameback:

• Therewere8,756femalesand6,010maleswhoresponded.• Outofallthemales,59.7%chosevanillaoverchocolate.• 4,732femaleschosechocolate.

1. Uponfirstobservations,whichflavordoyouthink“won”?_____________________.Writeasentencedescribingwhatyouseeat‘firstglance’thatmakesyouthinkthis.

2. Raquelstartedtoorganizethedatainthefollowingtwo-waytable.Seeifyoucanhelpcompletethis(usingcountsandnotpercentages):

3. OrganizethesamedatainaVenndiagramandatreediagram.

4. Usingyourorganizeddatarepresentations,writeprobabilitiesthathelpsupportyourclaimregardingthepreferredflavoroficecream.Foreachprobability,writeacomplete

statementaswellasthecorrespondingprobabilitynotation.

Chocolate Vanilla Total

Female 8,756

Male 6,010

Total

CCBYhttps://flic.kr/p/dAmJrc

5


PROBABILITY- 9.2


5. Lookingoverthethreerepresentations(treediagram,two-waytable,andVenndiagram),whatprobabilitiesseemtobeeasiertoseeineach?Whatprobabilitiesarehiddenorhard

tosee?

Highlighted(easiertosee) HiddenTreediagram

Treediagram

Two-waytable

Two-waytable

Venndiagram

Venndiagram

6. Gettingbacktoicecream.Doyouthinkthisisenoughinformationtoproclaimthestatementthatoneicecreamisfavoredoveranother?Explain.

6


PROBABILITY – 9.2




9.2


READY

Topic:AnalyzingdatagiveninaVennDiagram.

UsetheVennDiagramsbelowtoanswerthefollowingquestions.(Hint:youmayusethesamedataprovidedinthetwo-waytablefromquestion3onthenextpagetohelpmakesenseoftheVennDiagram)ThefollowingVennDiagramrepresentstherelationshipbetweenfavoritesport(SoccerorBaseball)andgender(FemaleorMale).

1.Howmanypeoplesaidsocceristheirfavoritesport?

2.Howmanyfemalesareinthedata?

3.Howmanymaleschosebaseball?

4.Whatistheprobabilitythatapersonwouldsaysocceristheir

favoritesport?P(soccer)=

5.Whatistheprobabilitythatafemalewouldsaysocceristheirfavoritesport?(“Outofallfemales,

____%saysocceristheirfavoritesport”)P(soccer|female)=

ThefollowingVennDiagramrepresentstherelationshipbetweenfavoritesubject(MathorScience)andgradelevel(NinthorTenth).Usingthisdata,answerthefollowingquestions.

6.Howmanypeoplesaidmathistheirfavoritesubject?

7.Howmanytenthgradersareinthedata?

8.Howmanyninthgraderschosescience?

9.Whatistheprobabilitythatapersonwouldsayscienceistheir

favoritesubject?P(s)=

10.Whatistheprobabilitythatatenthgraderwouldsayscienceistheirfavoritesubject?(“Ifyouarea

tenthgrader,thentheprobabilityofsciencebeingyourfavoritesubjectis_____%”)P(science|tenth)=


30

25

7


PROBABILITY – 9.2




9.2


SET Topic:Writingconditionalstatementsfromtwo-waytables

11.Completethetableandwritethreeconditionalstatements.

Soccer Baseball Total

Male 30

Female 50 76

Total 85

12.Completethetableaboutpreferredgenreofreadingandwritethreeconditionalstatements.

Fiction

Non-

Fiction

Total

Male 10

Female 50 60

Total 85

13.CompletethetableaboutfavoritecolorofM&M’sandwritethreeconditionalstatements.

Blue Green Red Other Total

Male 15 20 15 60

Female 30 20 10

Total 45 130

14.Usetheinformationprovidedtomakeatreediagram,atwo-waytableandaVennDiagram.

• Datawascollectedatthemovietheaterlastfall.Notaboutmoviesbutclothes.• 6,525peoplewereobserved.• 3,123hadonshortsandtheresthadonpants• 45%ofthosewearingshortsweredenim.• Ofthosewearingpants88%weredenim.

8


PROBABILITY – 9.2




9.2


GO Topic:BasicProbability

Findthedesiredvalues.

15.Whatishalfofone-third? 16.Whatisone-thirdoftwo-fifths?

17.Whatisone-fourthoffour-sevenths? 18.Whatpercentis!!?

19.Whatis35%of50? 20.Seventyis60%ofwhatnumber?

21.Write!!"asapercent. 22.Write

!!asapercent.

23.Whatis52%of1,200? 24.Whatpercentis32of160?

25.Sixtyiswhatpercentof250? 26.Whatpercentof350is50?

9


PROBABILITY- 9.3


9.3 Fried Freddy’s A Solidify Understanding Task

Daniellewassurprisedbytheresultsofthesurveytodetermine

the‘favoriteicecream’betweenchocolateandvanilla(Seetask

9.2Chocolatevs.Vanilla).Thereason,sheexplains,isthatshehadaskedseveralofherfriends

andtheresultswereasfollows:

1. Inthissituation,chocolateismostpreferred.Howwouldyouexplaintoherthatthisdata

maybeless‘valid’comparedtothedatafromtheprevioussurvey?

Usingasufficientlylargenumberoftrialshelpsusestimatetheprobabilityofaneventhappening.If

thesampleislargeenough,wecansaythatwehaveanestimatedprobabilityoutcomeforthe

probabilityofaneventhappening.Ifthesampleisnotrandomlyselected(onlyaskingyourfriends)

ornotlargeenough(collectingfourdatapointsisnotenoughinformationtoestimatelongrun

probabilities),thenoneshouldnotestimatelargescaleprobabilities.Sometimes,oursample

increasesinsizeovertime.Belowisanexampleofdatathatiscollectedovertime,sotheestimated

probabilityoutcomebecomesmorepreciseasthesampleincreasesovertime.

Freddylovesfriedfood.Hispassionfortheperfectfriedfoodrecipesledtohimopeningthe

restaurant,“FriedFreddies.”Histwomaindishesarefocusedaroundfishorchicken.Knowinghe

alsohadtoopenuphismenutopeoplewhoprefertohavetheirfoodgrilledinsteadoffried,he

createdthefollowingmenuboard:

Chocolate Vanilla Total

Female 23 10 33

Male 6 8 14

Total 29 18 47

CCBYhttps://flic.kr/p/9a7kMg

10


PROBABILITY- 9.3


Afterbeingopenforsixmonths,Freddyrealizedhewashavingmorefoodwastethanheshould

becausehewasnotpredictinghowmuchofeachheshouldprepareinadvance.Hisbusinessfriend,

Tyrell,saidhecouldhelp.

2. WhatinformationdoyouthinkTyrellwouldneed?

Luckily,FreddyusesacomputertotakeorderseachdaysoTyrellhadlotsofdatatopullfrom.AfterdeterminingtheaveragenumberofcustomersFreddyserveseachday,TyrellcreatedthefollowingVenndiagramtoshowFreddythefoodpreferenceofhiscustomers:

Tomakesenseofthediagram,Freddycomputedthefollowingprobabilitystatements:

3. Whatistheprobabilitythatarandomlyselectedcustomerwouldorderfish?

P(fish)=

Shadethepartofthediagramthatmodelsthissolution.

30%15%20%

Fried Fish

Choose dish: Chicken or Fish

Choose cooking preference: Grilled or Fried

35%

11


PROBABILITY- 9.3


4. Whatistheprobabilitythatarandomlyselectedcustomerwouldorderfried

fish?

P(fried∩fish)=P(friedandfish)=


5. Whatistheprobabilitythatapersonprefersfriedchicken?

P(fried∩chicken)=P(friedandchicken)=


6. Whatistheestimatedprobabilitythatarandomlyselectedcustomerwould

wanttheirfishgrilled?

P(grilledandfish)=P(____________________)=


7. IfFreddyserves100mealsatlunchonaparticularday,howmanyordersoffishshouldhe

preparewithhisfamousfriedrecipe?

8. Whatistheprobabilitythatarandomlyselectedpersonwouldchoosefishor

fried?

P(fried∪fish)=P(friedorfish)=Shadethepartofthediagramthatmodelsthissolution.

9. WhatistheprobabilitythatarandomlyselectedpersonwouldNOTchoose

fishorfried?


12


PROBABILITY – 9.3




9.3


READY

Topic:IndependentandDependentEventsInsomeofthesituationsdescribedbelowthefirsteventeffectsthesubsequentevent(dependentevents).Inotherseachoftheeventsiscompletelyindependentoftheothers(independentevents).Determinewhichsituationsaredependentandwhichareindependent.1. Acoinisflippedtwice.Thefirsteventisthefirstflipandthesecondeventisthenextflip.

2. Abagofmarblescontains3bluemarbles,6redmarblesand2yellowmarbles.Twoofthemarblesaredrawnoutofthebag.Thefirsteventisthefirstmarbletakenoutthesecondeventisthesecondmarbletakenout.

3. Anattempttofindtheprobabilityoftherebeingaright-handedoraleft-handedbatterattheplateinabaseballgame.Thefirsteventisthe1stbattertocometotheplate.Thesecondeventisthesecondplayertocomeuptotheplate.

4. Astandarddieisrolledtwice.Thefirsteventisthefirstrollandthesecondeventisthesecondroll.

5. Twocardsaredrawnfromastandarddeckofcards.Thefirsteventisthefirstcardthatisdrawnthesecondeventisthesecondcardthatisdrawn.

SET Topic:AdditionRule,InterpretingaVennDiagram6.SallywasassignedtocreateaVenndiagramtorepresent!(! or !).Sallyfirstwrites!(! or !) = !(!) + !(!) − !(! and !),whatdoesthismean?Explaineachpart.

7.Sallythencreatesthefollowingdiagram.

Sally’sVenndiagramisincorrect.Why?


13


PROBABILITY – 9.3




9.3


TheVenndiagramtotherightshowsthedatacollectedatasandwichshopforthelastsixmonthswithrespecttothetypeofbreadpeopleordered(sourdoughorwheat)andwhetherornottheygotcheeseontheirsandwich.Usethisdatatocreateatwo-wayfrequencytableandanswerthequestions.

8.Two-wayfrequencytable

9. Whatistheprobabilitythatarandomlyselectedcustomerwouldordersourdoughbread?

P(sourdoughbread)=10. Whatistheprobabilitythatarandomlyselectedcustomerwouldordersourdoughbreadwithout

cheese?P(sourdough∩nocheese)=P(sourdoughandnocheese)=

11. Whatistheprobabilitythatapersonpreferswheatbreadwithoutcheese?P(wheat∩nocheese)=P(wheatandnocheese)=

12. Whatistheestimatedprobabilitythatarandomlyselectedcustomerwouldwanttheirsandwichwithcheese?P(sourdoughcheeseandwheatcheese)=P(____________________)=

13. Iftheyserve100sandwichesatlunchonaparticularday,howmanyorderswithsourdoughshouldbepreparedwithoutcheese?

14. Whatistheprobabilitythatarandomlyselectedpersonwouldchoosesourdoughorwithoutcheese?P(sourdough∪nocheese)=P(sourdoughornocheese)=

15. WhatistheprobabilitythatarandomlyselectedpersonwouldNOTchoosesourdourghornocheese?

20%

14


PROBABILITY – 9.3




9.3


GO Topic:EquivalentRatiosandProportionsUsethegivenratiotosetupaproportionandfindthedesiredvalue.

16. If3outof5studentseatschoollunchthenhowmanystudentswouldbeexpectedtoeatschool

lunchataschoolwith750students?

17. Inawelldevelopedandcarriedoutsurveyitwasfoundthat4outof10studentshaveapairofsunglasses.Howmanystudentswouldyouexpecttohaveapairofsunglassesoutofagroupof45students?

18. Datacollectedatalocalmallindictedthat7outof20menobservedwerewearingahat.Howmanywouldyouexpecttohavebeenwearinghatsif7500menweretobeatthemallonasimilarday?

15


PROBABILITY-9.1


Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

9.4 Visualizing with Venn

A Solidify Understanding Task OneoftheattributesofVenndiagram’sisthatitcanbeeasytoseetherelationshipswithinthedata.Inthistask,wewillcreatemultipleVenndiagramsusingdataanddeterminetheeventsthatcreatediagramstoeitherhaveanintersectionorforthemtobemutuallyexclusive.1. ThefollowingdatarepresentsthenumberofmenandwomenpassengersaboardtheTitanicand

whetherornottheysurvived.Fillintheblanksforthistable:

Survived Didnotsurvive Total

Men 659 805

Women 296

Total 442 765 1207

2. Usingthedataabove,createaVenndiagramforeachofthefollowing:a. MenvsWomen b. WomenvsSurvivedc. Youchoosetheconditions

3. CreatetwoprobabilitystatementsusingeachofyourVenndiagramsfromquestion2.

4. CreateandlabelthreedifferentVenndiagramsusingthefollowingdata.Createatleastonethatismutuallyexclusiveandatleastonethathasanintersection.Samplesize:100

P(girl)= !"!""P(girlorart)=( !"!"" +

!"!"") −

!"!""

P(art)= !"!""P(notart)=P(boy)=

5. DescribetheconditionsthatcreatemutuallyexclusiveVenndiagramsandthosethatcreateintersections.

6. WhatconjecturecanyoumakeregardingthebestwaytocreateaVenndiagramfromdatatohighlightprobabilities?

CC B

Y h

ttps

://fli

c.kr

/p/9

a7kM

g

16


PROBABILITY – 9.4




9.4


READY

Topic:Productsofprobabilities,multiplyinganddividingfractionsFindtheproductsorquotientsbelow.

1. 12 ∙23

2. 35 ∙13

3. 710 ∙

25

4. 87 ∙34

5. 1312

6. 25 ÷

23

7. P(A)=!!P(B)=

!!

P(A)∗P(B)=

8. P(A)=!!P(B)=!!

P(A)∗P(B)=

SET Topic:ConnectingrepresentationsofeventsforprobabilityForeachsituation,oneoftherepresentations(two-waytable,Venndiagram,treediagram,contextorprobabilitynotation)isprovided.Usetheprovidedinformationtocompletetheremainingrepresentations.9.AreyouBlue?

Notation 2-wayTableKey:Male=MFemale=FBlue=BNotBlue=NSamplesize=200P(B)=84/200P(M)=64/200P(F|B)=48/84P(B|F)=P(M∩B)=P(M∪B)=

Blue NotBlue

Total

Male

Female

Total

(Continuedonthenextpage)


17


PROBABILITY – 9.4




9.4


(Continued from the last page)

VennDiagram TreeDiagram

Writethreeobservationsyoucanmakeaboutthisdata.

10.Rightandlefthandednessofagroup.Notation 2-wayTable

Key:Male=MFemale=FLefty=LRighty=RSamplesize=100peopleP(L)=P(M)=P(F)=P(L|F)=P(L|M)=

Lefty Righty Total

Male

Female

Total


Writethreeconditionalstatementsregardingthisdata.

18


PROBABILITY – 9.4




9.4


11.Themostimportantmealoftheday.Notation 2-wayTable

Key:Male=MFemale=FEatsBreakfast=EDoesn’tEatBreakfast=DSamplesize=P(E)=P(E|M)=P(E∩M)=P(E|F)=P(E∩F)=

Eats Doesn’t Total

Male

Female

Total 685


Doesthisdatasurpriseyou?Whyorwhynot.

GO Topic:Writingconditionalstatementsfromtwo-waytables12.Completethetableandwritethreeconditionalstatements.

Biking Swimming TotalMale 50 Female 35 76Total 85

13.Completethetableaboutpreferredgenreofreadingandwritethreeconditionalstatements.

IceCream

Cake Total

Male 20 Female 10 60Total 85

14.Completethetableabouteyecolorandwritethreeconditionalstatements. Blue Green Brown Other Total

Male 55 20 15 100Female 20 10 Total 75 230

19


PPOBABILITY- 9.5


9.5 Freddy Revisited A Solidify Understanding Task

Intask9.3FriedFreddy’s,TyrellhelpedFreddyin

determiningtheamountandtypeoffoodFreddyshouldprepareeachdayforhisrestaurant.Asa

result,Freddy’sfoodwastedecreaseddramatically.Astimewentby,Freddynoticedthatanother

factorheneededtoconsiderwasthedayoftheweek.Henoticedthathewasoverpreparingduring

theweekandsometimesunderpreparingontheweekend.TyrellandFreddyworkedtogetherand

startedcollectingdatatofindtheaveragenumberofordershereceivedofchickenandfishona

weekdayandcomparedittotheaveragenumberofordershereceivedofeachontheweekend.

Aftertwomonths,theyhadenoughinformationtocreatethetwowaytablebelow:

Fish Chicken TotalWeekday 65 79 144Weekend 88 107 195Total 153 186 339

1. Whatobservationscanbemadefromthetable(includeprobabilitystatements)?

2. Whatdoyounoticeabouttheprobabilitystatements?

3. Basedonthedata,ifFreddyhadasalespromotionandanticipated500ordersinagivenweek,howmanyofeach(chickenandfish)shouldheorder?

CcbyNicoleAbaldi

http://flic.kr/p/dBMGid

20


PROBABILITY – 9.5




9.5


READY

Topic:QuadraticfunctionsFindthex-intercepts,y-intercept,lineofsymmetryandvertexforthequadraticfunctions.

1.!(!) = !! + 8!– 9

2.! ! = !!– 3! – 5 3.ℎ ! = 2!! + 5! − 3

4.!(!) = !! + 6! – 9 5.!(!) = (! + 5)!– 2 6.!(!) = (! + 7)(! – 5)

SET Topic:IndependenceDeterminingtheindependenceofeventscansometimesbedonebybecomingfamiliarwiththecontextinwhichtheeventsoccurandthenatureoftheevents.Therearealsosomewaysofdeterminingindependenceofeventsbasedonequivalentprobabilities.

• Twoevents,AandB,areindependentifP(AandB)=P(A)∙P(B)• Additionally,twoevents,AandB,areindependentifP(A|B)=!(! !"# !)!(!) =P(A)

Usethesetwowaysofdeterminingindependenteventstodetermineindependenceintheproblemsbelowandanswerthequestions.

7.P(AandB)=!!

P(A)=!!P(B)= !!"

8.P(A)=!!

P(AandB)=!!

P(B)=!!

9.P(A)=!!

P(AandB)=!!

P(B)=!!

10.P(AandB)=!!

P(A)=!!P(B)=!!


21


PROBABILITY – 9.5




9.5


GO Topic:FindProbabilitiesfromatwo-waytableThefollowingdatarepresentsthenumberofmenandwomenpassengersaboardthetitanicandwhetherornottheysurvived.

Survived Didnotsurvive Total

Men 146 659 805

Women 296 106 402

Total 442 765 1207

11. P(w)=

12. P(s)=

13. P(s|w)=

14. P(wors)=

15. P(worm)=

16. P(ns|w)=

17. P(m∩ns)=

22


PPOBABILITY- 9.6


9.6 Striving for Independence A Practice Understanding Task

Answerthequestionsbelowusingyourknowledgeofconditional

probability(theprobabilityofAgivenBasP(AandB)/P(B))as

wellasthedefinitionofindependence.Twoevents(AandB)aresaidtobeindependentif

! !|! = ! ! !"# ! !|! = !(!).Keeptrackofhowyouaredeterminingindependenceforeachtypeofrepresentation.

1. Outofthe2000studentswhoattendacertainhighschool,1400studentsowncellphones,

1000ownatablet,and800haveboth.CreateaVenndiagrammodelforthissituation.Use

properprobabilitynotationasyouanswerthequestionsbelow.

a) Whatistheprobabilitythatarandomlyselectedstudentownsacellphone?

b) Whatistheprobabilitythatarandomlyselectedstudentsownsbothacellphoneanda

tablet?

c) Ifarandomlyselectedstudentownsacellphone,whatistheprobabilitythatthis

studentalsoownsatablet?

d) Howarequestionsbandcdifferent?

e) Aretheoutcomes,ownsacellphoneandownsatablet,independent?Explain.

2. BelowisapartiallycompletedtreediagramfromthetaskChocolatevsVanilla.

a) Circlethepartsofthediagramthatwouldbeusedtodetermineifchoosingchocolateis

independentofbeingamaleorfemale.

b) Completethediagramsothatchoosingchocolateisindependentofbeingmaleorfemale.

http://www.flickr.com

/photos/ronw

ls/

23


PPOBABILITY- 9.6


3. UsethedatafromtheTitanticbelowtoanswerthefollowingquestions.

Survived Didnotsurvive TotalMen 146 659 805Women 296 106 402Total 442 765 1207

a) Determineifsurvivalisindependentofbeingmaleforthisdata.Explainorshowwhyor

whynot.Ifitisnotindependentdeterminehowmanymenwouldneedtosurvivein

ordertomakeitindependent.

4. Determinewhetherthesecondscenariowouldbedependentorindependentofthefirst

scenario.Explain.

a) Rollingasix-sideddie,thendrawingacardfromadeckof52cards.

b) Drawingacardfromadeckof52cards,thendrawinganothercardfromthesamedeck.

c) Rollingasix-sideddie,thenrollingitagain.

d) Pullingamarbleoutofabag,replacingit,thenpullingamarbleoutofthesamebag.

e) Having20treatsinfivedifferentflavorsforasoccerteam,witheachplayertakinga

treat.

24


PROBABILITY – 9.6




9.6


READY

Topic:SolvingquadraticsSolveeachofthequadraticsbelowusinganappropriatemethod.

1.m2+15m+56=0 2.5x2–3x+7=0

3.x2−10x+21=0 4.6x2+7x–5=0

SET Topic:RepresentingIndependentEventsinVennDiagramsIneachoftheVennDiagramsthenumberofoutcomesforeacheventaregiven,usetheprovidedinformationtodeterminetheconditionalprobabilitiesorindependence.ThenumbersintheVennDiagramindicatethenumberofoutcomesinthatpartofthesamplespace.5.

a.Howmanytotaloutcomesarepossible?b.P(A)=c.P(B)=d.P(A∩B)=e.P(A|B)=

f.AreeventsAandBindependentevents?Whyorwhynot?


25


PROBABILITY – 9.6




9.6


6.

a.Howmanytotaloutcomesarepossible?b.P(E)=c.P(F)=d.P(E∩F)=e.P(E|F)=

f.AreeventsEandFindependentevents?Whyorwhynot?7.

a.Howmanytotaloutcomesarepossible?b.P(X)=c.P(Y)=d.P(X∩Y)=e.P(X|Y)=

f.AreeventsXandYindependentevents?Whyorwhynot?8.

a.Howmanytotaloutcomesarepossible?b.P(K)=c.P(L)=d.P(K∩L)=e.P(K|L)=

f.AreeventsKandLindependentevents?Whyorwhynot?

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PROBABILITY – 9.6




9.6


GO Topic:ConditionalProbabilityandIndependenceDatagatheredontheshoppingpatternsduringthemonthsofAprilandMayofhighschoolstudentsfromPeanutVillagerevealedthefollowing.38%ofstudentspurchasedanewpairofshorts(callthiseventH),15%ofstudentspurchasedanewpairofsunglasses(callthiseventG)and6%ofstudentspurchasedbothapairofshortandapairofsunglasses.9.Findtheprobabilitythatastudentpurchasedapairofsunglassesgiventhatyouknowtheypurchasedapairofshorts.P(G|H)=10.Findtheprobabilitythatastudentpurchasedapairofshortsorpurchasedanewpairofsunglasses.P(H∪G)=11.Giventheconditionthatyouknowastudenthaspurchasedatleastoneoftheitems.Whatistheprobabilitythattheypurchasedonlyoneoftheitems?12.ArethetwoeventsHandGindependentofoneanother?WhyorWhynot?Giventhedatacollectedfrom200individualsconcerningwhetherornottoextendthelengthoftheschoolyearinthetablebelowanswerthequestions.

For Against NoOpinion Youth(5to19) 7 35 12 Adults(20to55) 30 27 20 Seniors(55+) 25 16 28

20013.Giventhatconditionthatapersonisanadultwhatistheprobabilitythattheyareinfavorofextendingtheschoolyear?P(For|Adult)=14.GiventheconditionthatapersonisagainstextendingtheschoolyearwhatistheprobabilitytheyareaSenior?P(Senior|Against)=15.Whatistheprobabilitythatapersonhasnoopiniongiventhattheyareayouth?P(noopinion|youth)=

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working ST Core Reg - Mathematics Vision Project · SECONDARY MATH II // MODULE 9 PROBABILITY- 9.2 Mathematics Vision Project 9.2 Chocolate versus Vanilla A Solidify Understanding

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