Welcome! U4H2: Worksheet–#’s2-7,9-13,16,20

Updates: U4Tis12/12Announcement: December 16th is the last day I will accept late work.

Agenda ① Review U4H1 ② Theoretical Probability ③ Experimental Probability ④ Cool-Down!

Review U4H1

Warm-Up! (1) Compare. Write >, <, or =. (a) 7P4 7P3

(b) 7P3 7C4

Warm-Up! (2) How many ways can you choose a manager and assistant from a 9-person task force?

72 (3) There are 5 airplanes ready to depart. Runway A and runway D are available. How many ways can 2 planes be assigned to runways without using the same runway?

20

SettingupyourNotebookLeaveonepageblankforsupplementalnotes.

Today’sLesson#:----Topic:Theoreticalvs.ExperimentalProbabilityLO#2:Determinethetheoreticalorexperimentalprobabilityofanevent.

ProbabilityProbability•  Themeasureofhowlikelyaneventistooccur.•  Eachpossibleresultofaprobabilityexperimentorsituationisanoutcome.

•  Thesetofallpossibleoutcomesisthesamplespace.•  Aneventisanoutcomeorsetofoutcomes.

ProbabilityProbability•  Writtenasafractionordecimalfrom0to1,oraspercent'sfrom0%to100%.

ProbabilityTypesofOutcomes•  Equallylikelyoutcomes

– Havethesamechanceofoccurring.– Example:Youtossafaircoin,headsandtailsareequallylikelyoutcomes.

•  Favorableoutcomes–  OutcomesinaspeciWiedevent.–  Example:Youtossafaircoin,whatistheprobabilityoflandingonatails?Thefavorableoutcomesforatailsis1.

TheoreticalProbabilityTheoreticalProbability•  Itisthelikelinessofaneventhappeningbasedonallthepossibleoutcomes.

•  Aneventistheratioofthenumberoffavorableoutcomestothetotalnumberofoutcomes.

TheoreticalProbabilityPractice:(1)EachletterofthewordPROBABLEiswrittenonaseparatecard.Thecardsareplacedfacedownandmixedup.Whatistheprobabilitythatarandomlyselectedcardhasaconsonant?(2)Twonumbercubesarerolled.Whatistheprobabilitythatthedifferencebetweenthetwonumbersis4?(3)Arednumbercubeandabluenumbercubearerolled.Ifallnumbersareequallylikely,whatistheprobabilityoftheevent?Thedifferenceis6.

TheoreticalProbability

TheoreticalProbabilityPractice:(4)Agumballmachinecontains20yellowgumballs,12greengumballs,and13pinkgumballs.Whatistheprobabilitythatthenextgumballthatcomesoutwillbeeitheryelloworgreen?(5)Youpickonecardfromastandarddeck.Whatistheprobabilitythatthecardwillnotbearedcard?(6)Ajarcontains3blue,6green,and2redmarbles.Ifyoupickonewithoutlooking,whatistheprobabilitythatthemarbleyoupickwillbeneitherbluenorgreen?

TheoreticalProbabilityComplement•  ThecomplementofaneventEisthesetofalloutcomesinthesamplespacethatarenotinE.

TheoreticalProbabilityPractice:(7)Thereare25studentsinstudyhall.Thetableshowsthenumberofstudentswhoarestudyingaforeignlanguage.Whatistheprobabilitythatarandomlyselectedstudentisnotstudyingaforeignlanguage?(8)Twointegersfrom1to10arerandomlyselected.Thesamenumbermaybechosentwice.Whatistheprobabilitythatbothnumbersarelessthan9?

Language Number French 6 Spanish 12

Japanese 3

TheoreticalProbabilityPractice:(9)Eachstudentreceivesa5-digitlockercombination.Whatistheprobabilityofreceivingacombinationwithallodddigits?

TheoreticalProbabilityGeometricProbability•  Aformoftheoreticalprobability.•  P(apointchosenatrandomin…)=theareaorvolumethatyouwantdividedbytheareaorvolumeoftheentireWigure.

TheoreticalProbabilityPractice:(10)AWigureiscreatedplacingarectangleinsideatriangleinsideasquareasshown.IfapointinsidetheWigureischosenatrandom,whatistheprobabilitythatthepointisinsidetheshadedregion?(11)Findtheprobabilitythatapointchosenatrandominsidethelargetriangleisinthesmalltriangle.

ExperimentalProbabilityExperientialProbability•  Isoftenusedtoestimatetheoreticalprobabilityandtomakepredictions.

•  Eachrepetitionofanexperimentisatrial.– Example:Samrolledanumbercube50times.A3appeared10times.Thentheexperimentalprobabilityofrollinga3is10outof50or20%.

ExperimentalProbabilityPractice:(12)Thetableshowstheresultsofaspinnerexperiment.Findtheexperimentalprobabilityofspinninga4.(13)Thetableshowstheresultsofchoosingonecardfromadeckofcards,recordingthesuit,andthenreplacingthecard.Findtheexperimentalprobabilityofchoosingadiamond.

Number Occurrences

1 6

2 11

3 19

4 14

ExperimentalProbabilityPractice:Identifythetypeofprobabilitybeingused(theoretical,complement,geometric,orexperimental).Answerthequestion.(14)Inaboxof25switches,3aredefective.Whatistheprobabilityofrandomlyselectingaswitchthatisnotdefective? (15)Thereare12E’samongthe100tilesinScrabble.Whatistheprobabilityofselectingall4E’swhenselecting4tiles?

ExperimentalProbability(16)Thetableshowstheresultsofrollingadiewithunequalfaces.Findtheexperimentalprobabilityofrolling1or6.(17)Afruitbowlcontains4greenapplesand7redapples.Whatistheprobabilitythatarandomlyselectedapplewillbegreen?

ExperimentalProbability(18)JoanneisguessingwhichdayinNovemberisBess’sbirthday.JoanneknowsthatBess’sbirthdaydoesnotfallonanodd-numberedday.WhatistheprobabilitythatJoannewillguessthecorrectdayonherWirsttry?(19)Tomhasadollar’sworthofdimesandadollar’sworthofnickelsinhispocket.a.Whatistheprobabilityhewillrandomlyselectanickelfromhispocket?b.Whatistheprobabilityhewillrandomlyselectadimefromhispocket?

Cool-Down!Onyourwhiteboardwewilldothefollowingpractice:h)p://my.hrw.com/math06_07/nsmedia/prac>ce_quizzes/

alg2/alg2_pq_prs_02.html