分析报告2ppt课件.ppt

3 1 Chapter3 Probability 3 2 Outline 3 1Introduction3 2Fundamentals3 3AdditionRulesforProbability3 4MultiplicationRules Basics3 5MultiplicationRules BeyondtheBasics 3 3 Objectives DetermineSampleSpacesandfindtheprobabilityofaneventusingclassicalprobability Findtheprobabilityofaneventusingempiricalprobability Findtheprobabilityofcompoundeventsusingtheadditionrules 3 4 Objectives Findtheprobabilityofcompoundeventsusingthemultiplicationrules Findtheconditionalprobabilityofanevent 3 5 3 2Fundamentals Aprobabilityexperimentisaprocessthatleadstowell definedresultscalledoutcomes Anoutcomeistheresultofasingletrialofaprobabilityexperiment NOTE Atreediagramcanbeusedasasystematicwaytofindallpossibleoutcomesofaprobabilityexperiment 3 6 3 2TreeDiagramforTossingTwoCoins FirstToss 3 7 3 2SampleSpaces Examples 3 8 3 2FormulaforClassicalProbability Classicalprobabilityassumesthatalloutcomesinthesamplespaceareequallylikelytooccur Thatis equallylikelyeventsareeventsthathavethesameprobabilityofoccurring 3 9 3 2FormulaforClassicalProbability 3 10 3 2ClassicalProbability Examples Foracarddrawnfromanordinarydeck findtheprobabilityofgetting a aqueen b a6ofclubs c a3oradiamond Solution a Sincethereare4queensand52cards P queen 4 52 1 13 b Sincethereisonlyone6ofclubs thenP 6ofclubs 1 52 3 11 3 2ClassicalProbability Examples c Therearefour3sand13diamonds butthe3ofdiamondsiscountedtwiceinthelisting Hencethereareonly16possibilitiesofdrawinga3oradiamond thusP 3ordiamond 16 52 4 13 3 12 3 2ClassicalProbability Examples Whenasingledieisrolled findtheprobabilityofgettinga9 Solution Sincethesamplespaceis1 2 3 4 5 and6 itisimpossibletogeta9 Hence P 9 0 6 0 NOTE Thesumoftheprobabilitiesofalloutcomesinasamplespaceisone 3 13 3 2ComplementofanEvent E 3 14 3 2ComplementofanEvent Example Findthecomplementofeachevent Rollingadieandgettinga4 Solution Gettinga1 2 3 5 or6 Selectingaletterofthealphabetandgettingavowel Solution Gettingaconsonant assumeyisaconsonant 3 15 3 2ComplementofanEvent Example Selectingadayoftheweekandgettingaweekday Solution GettingSaturdayorSunday Selectingaone childfamilyandgettingaboy Solution Gettingagirl 3 16 3 2RuleforComplementaryEvent P E P E or P E P E or P E P E 1 1 1 3 17 3 2EmpiricalProbability Thedifferencebetweenclassicalandempiricalprobabilityisthatclassicalprobabilityassumesthatcertainoutcomesareequallylikelywhileempiricalprobabilityreliesonactualexperiencetodeterminetheprobabilityofanoutcome 3 18 3 2FormulaforEmpiricalProbability 3 19 3 2EmpiricalProbability Example Inasampleof50people 21hadtypeOblood 22hadtypeAblood 5hadtypeBblood and2hadABblood Setupafrequencydistribution 3 20 3 2EmpiricalProbability Example Type Frequency ABABO 225221 50 n 3 21 3 2EmpiricalProbability Example Findthefollowingprobabilitiesforthepreviousexample ApersonhastypeOblood Solution P O f n 21 50 ApersonhastypeAortypeBblood Solution P AorB 22 50 5 50 27 50 3 22 3 3AdditionRulesforProbability Twoeventsaremutuallyexclusiveiftheycannotoccuratthesametime i e theyhavenooutcomesincommon 3 23 3 3TheAdditionRulesforProbability A B AandBaremutuallyexclusive 3 24 3 3AdditionRule1 WhentwoeventsAandBaremutuallyexclusive theprobabilitythatAorBwilloccuris 3 25 3 3AdditionRule1 Example Atapoliticalrally thereare20Liberals L 13Conservatives C and6NDPs N Ifapersonisselected findtheprobabilitythatheorsheiseitheraConservativeoranNDP Solution P CorN P C P N 13 39 6 39 19 39 3 26 3 3AdditionRule1 Example Adayoftheweekisselectedatrandom Findtheprobabilitythatitisaweekend Solution P SaturdayorSunday P Saturday P Sunday 1 7 1 7 2 7 3 27 3 3AdditionRule2 WhentwoeventsAandB arenotmutuallyexclusive the probability y that A or B will occur is P A or B P A P B P A and B 3 28 3 3AdditionRule2 A B AandB commonportion 3 29 3 3AdditionRule2 Example Inahospitalunitthereareeightnursesandfivephysicians Sevennursesandthreephysiciansarefemales Ifastaffpersonisselected findtheprobabilitythatthesubjectisanurseoramale Thenextslidehasthedata 3 30 3 3AdditionRule2 Example 3 31 3 3AdditionRule2 Example Solution P nurseormale P nurse P male P malenurse 8 13 3 13 1 13 10 13 3 32 3 3AdditionRule2 Example OnNewYear sEve theprobabilitythatapersondrivingwhileintoxicatedis0 32 theprobabilityofapersonhavingadrivingaccidentis0 09 andtheprobabilityofapersonhavingadrivingaccidentwhileintoxicatedis0 06 Whatistheprobabilityofapersondrivingwhileintoxicatedorhavingadrivingaccident 3 33 3 3AdditionRule2 Example Solution P intoxicatedoraccident P intoxicated P accident P intoxicatedandaccident 0 32 0 09 0 06 0 35 3 34 TwoeventsAandBareindependentifthefactthatAoccursdoesnotaffecttheprobabilityofBoccurring Example Rollingadieandgettinga6 andthenrollinganotherdieandgettinga3areindependentevents 3 4TheMultiplicationRulesandConditionalProbability 3 35 3 4MultiplicationRules 3 36 3 4MultiplicationRule1 Example Acardisdrawnfromadeckandreplaced thenasecondcardisdrawn Findtheprobabilityofgettingaqueenandthenanace Solution Becausethesetwoeventsareindependent why P queenandace 4 52 4 52 16 2704 1 169 3 37 3 4MultiplicationRule1 Example ADecimapolefoundthat46 ofCanadianssaytheysuffergreatstressatleastonceaweek Ifthreepeopleareselectedatrandom findtheprobabilitythatallthreewillsaythattheysufferstressatleastonceaweek Solution LetSdenotestress ThenP SandSandS 0 46 3 0 097 3 38 3 4MultiplicationRule1 Example Theprobabilitythataspecificmedicaltestwillshowpositiveis0 32 Iffourpeoplearetested findtheprobabilitythatallfourwillshowpositive Solution LetTdenoteapositivetestresult ThenP TandTandTandT 0 32 4 0 010 3 39 Whentheoutcomeoroccurrenceofthefirsteventaffectstheoutcomeoroccurrenceofthesecondeventinsuchawaythattheprobabilityischanged theeventsaresaidtobedependent Example Havinghighgradesandgettingascholarshiparedependentevents 3 5MultiplicationRules ConditionalProbability 3 40 TheconditionalprobabilityofaneventBinrelationshiptoaneventAistheprobabilitythataneventBoccursaftereventAhasalreadyoccurred ThenotationfortheconditionalprobabilityofBgivenAisP B A NOTE ThisdoesnotmeanB A 3 5MultiplicationRules ConditionalProbability 3 41 3 4MultiplicationRule2 3 42 Inashipmentof25microwaveovens twoaredefective Iftwoovensarerandomlyselectedandtested findtheprobabilitythatbotharedefectiveifthefirstoneisnotreplacedafterithasbeentested Solution Seenextslide 3 5TheMultiplicationRules ConditionalProbability Example 3 43 Solution Sincetheeventsaredependent P D1andD2 P D1 P D2 D1 2 25 1 24 2 600 1 300 3 5TheMultiplicationRulesandConditionalProbability Example 3 44 TheKWInsuranceCompanyfoundthat53 oftheresidentsofacityhadhomeowner sinsurancewithitscompany Oftheseclients 27 alsohadautomobileinsurancewiththecompany Ifaresidentisselectedatrandom findtheprobabilitythattheresidenthasbothhomeowner sandautomobileinsurance 3 5TheMultiplicationRulesandConditionalProbability Example 3 45 Solution Sincetheeventsaredependent P HandA P H P A H 0 53 0 27 0 1431 3 5TheMultiplicationRulesandConditionalProbability Example 3 46 Box1containstworedballsandoneblueball Box2containsthreeblueballsandoneredball Acoinistossed Ifitfallsheadsup box1isselectedandaballisdrawn Ifitfallstailsup box2isselectedandaballisdrawn Findtheprobabilityofselectingaredball 3 5TheMultiplicationRulesandConditionalProbability Example 3 47 3 5TreeDiagramforExample 3 48 Solution P red 1 2 2 3 1 2 1 4 2 6 1 8 8 24 3 24 11 24 3 5TheMultiplicationRulesandConditionalProbability Example 3 49 3 5ConditionalProbability Formula 3 50 TheprobabilitythatSamparksinano parkingzoneandgetsaparkingticketis0 06 andtheprobabilitythatSamcannotfindalegalparkingspaceandhastoparkintheno parkingzoneis0 2 OnTuesday Samarrivesatschoolandhastoparkinano parkingzone Findtheprobabilitythathewillgetati