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Welcome! U4H2: Worksheet–#’s2-7,9-13,16,20
Updates: U4Tis12/12Announcement: December 16th is the last day I will accept late work.
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Agenda ① Review U4H1 ② Theoretical Probability ③ Experimental Probability ④ Cool-Down!
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Review U4H1
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Warm-Up! (1) Compare. Write >, <, or =. (a) 7P4 7P3
(b) 7P3 7C4
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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
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SettingupyourNotebookLeaveonepageblankforsupplementalnotes.
Today’sLesson#:----Topic:Theoreticalvs.ExperimentalProbabilityLO#2:Determinethetheoreticalorexperimentalprobabilityofanevent.
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ProbabilityProbability• Themeasureofhowlikelyaneventistooccur.• Eachpossibleresultofaprobabilityexperimentorsituationisanoutcome.
• Thesetofallpossibleoutcomesisthesamplespace.• Aneventisanoutcomeorsetofoutcomes.
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ProbabilityProbability• Writtenasafractionordecimalfrom0to1,oraspercent'sfrom0%to100%.
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ProbabilityTypesofOutcomes• Equallylikelyoutcomes
– Havethesamechanceofoccurring.– Example:Youtossafaircoin,headsandtailsareequallylikelyoutcomes.
• Favorableoutcomes– OutcomesinaspeciWiedevent.– Example:Youtossafaircoin,whatistheprobabilityoflandingonatails?Thefavorableoutcomesforatailsis1.
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TheoreticalProbabilityTheoreticalProbability• Itisthelikelinessofaneventhappeningbasedonallthepossibleoutcomes.
• Aneventistheratioofthenumberoffavorableoutcomestothetotalnumberofoutcomes.
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TheoreticalProbabilityPractice:(1)EachletterofthewordPROBABLEiswrittenonaseparatecard.Thecardsareplacedfacedownandmixedup.Whatistheprobabilitythatarandomlyselectedcardhasaconsonant?(2)Twonumbercubesarerolled.Whatistheprobabilitythatthedifferencebetweenthetwonumbersis4?(3)Arednumbercubeandabluenumbercubearerolled.Ifallnumbersareequallylikely,whatistheprobabilityoftheevent?Thedifferenceis6.
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TheoreticalProbability
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TheoreticalProbabilityPractice:(4)Agumballmachinecontains20yellowgumballs,12greengumballs,and13pinkgumballs.Whatistheprobabilitythatthenextgumballthatcomesoutwillbeeitheryelloworgreen?(5)Youpickonecardfromastandarddeck.Whatistheprobabilitythatthecardwillnotbearedcard?(6)Ajarcontains3blue,6green,and2redmarbles.Ifyoupickonewithoutlooking,whatistheprobabilitythatthemarbleyoupickwillbeneitherbluenorgreen?
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TheoreticalProbabilityComplement• ThecomplementofaneventEisthesetofalloutcomesinthesamplespacethatarenotinE.
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TheoreticalProbabilityPractice:(7)Thereare25studentsinstudyhall.Thetableshowsthenumberofstudentswhoarestudyingaforeignlanguage.Whatistheprobabilitythatarandomlyselectedstudentisnotstudyingaforeignlanguage?(8)Twointegersfrom1to10arerandomlyselected.Thesamenumbermaybechosentwice.Whatistheprobabilitythatbothnumbersarelessthan9?
Language Number French 6 Spanish 12
Japanese 3
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TheoreticalProbabilityPractice:(9)Eachstudentreceivesa5-digitlockercombination.Whatistheprobabilityofreceivingacombinationwithallodddigits?
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TheoreticalProbabilityGeometricProbability• Aformoftheoreticalprobability.• P(apointchosenatrandomin…)=theareaorvolumethatyouwantdividedbytheareaorvolumeoftheentireWigure.
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TheoreticalProbabilityPractice:(10)AWigureiscreatedplacingarectangleinsideatriangleinsideasquareasshown.IfapointinsidetheWigureischosenatrandom,whatistheprobabilitythatthepointisinsidetheshadedregion?(11)Findtheprobabilitythatapointchosenatrandominsidethelargetriangleisinthesmalltriangle.
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ExperimentalProbabilityExperientialProbability• Isoftenusedtoestimatetheoreticalprobabilityandtomakepredictions.
• Eachrepetitionofanexperimentisatrial.– Example:Samrolledanumbercube50times.A3appeared10times.Thentheexperimentalprobabilityofrollinga3is10outof50or20%.
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ExperimentalProbabilityPractice:(12)Thetableshowstheresultsofaspinnerexperiment.Findtheexperimentalprobabilityofspinninga4.(13)Thetableshowstheresultsofchoosingonecardfromadeckofcards,recordingthesuit,andthenreplacingthecard.Findtheexperimentalprobabilityofchoosingadiamond.
Number Occurrences
1 6
2 11
3 19
4 14
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ExperimentalProbabilityPractice:Identifythetypeofprobabilitybeingused(theoretical,complement,geometric,orexperimental).Answerthequestion.(14)Inaboxof25switches,3aredefective.Whatistheprobabilityofrandomlyselectingaswitchthatisnotdefective? (15)Thereare12E’samongthe100tilesinScrabble.Whatistheprobabilityofselectingall4E’swhenselecting4tiles?
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ExperimentalProbability(16)Thetableshowstheresultsofrollingadiewithunequalfaces.Findtheexperimentalprobabilityofrolling1or6.(17)Afruitbowlcontains4greenapplesand7redapples.Whatistheprobabilitythatarandomlyselectedapplewillbegreen?
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ExperimentalProbability(18)JoanneisguessingwhichdayinNovemberisBess’sbirthday.JoanneknowsthatBess’sbirthdaydoesnotfallonanodd-numberedday.WhatistheprobabilitythatJoannewillguessthecorrectdayonherWirsttry?(19)Tomhasadollar’sworthofdimesandadollar’sworthofnickelsinhispocket.a.Whatistheprobabilityhewillrandomlyselectanickelfromhispocket?b.Whatistheprobabilityhewillrandomlyselectadimefromhispocket?
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Cool-Down!Onyourwhiteboardwewilldothefollowingpractice:h)p://my.hrw.com/math06_07/nsmedia/prac>ce_quizzes/
alg2/alg2_pq_prs_02.html