Post on 13-Aug-2020
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