Copyright©2009CengageLearning6.1ChapterSixProbabilityCopyright©2009CengageLearning6.2ApproachestoAssigningProbabilities…Therearethreewaystoassignaprobability,P(Oi),toanoutcome,Oi,namely:Classicalapproach:basedonequallylikelyevents.Relativefrequency:assigningprobabilitiesbasedonexperimentationorhistoricaldata.Subjectiveapproach:Assigningprobabilitiesbasedontheassignor’s(subjective)judgment.Copyright©2009CengageLearning6.3ClassicalApproach…Ifanexperimenthasnpossibleoutcomes,thismethodwouldassignaprobabilityof1/ntoeachoutcome.Itisnecessarytodeterminethenumberofpossibleoutcomes.Experiment:RollingadieOutcomes{1,2,3,4,5,6}Probabilities:Eachsamplepointhasa1/6chanceofoccurring.Copyright©2009CengageLearning6.4ClassicalApproach…Experiment:RollingtwodiceandobservingthetotalOutcomes:{2,3,…,12}Examples:P(2)=1/36P(6)=5/36P(10)=3/36123456123456723456783456789456789105678910116789101112Copyright©2009CengageLearning6.5RelativeFrequencyApproach…Bits&BytesComputerShoptracksthenumberofdesktopcomputersystemsitsellsoveramonth(30days):Forexample,10daysoutof302desktopsweresold.Fromthiswecanconstructtheprobabilitiesofanevent(i.e.the#ofdesktopsoldonagivenday)…DesktopsSold#ofDays011221031245Copyright©2009CengageLearning6.6RelativeFrequencyApproach…“Thereisa40%chanceBits&Byteswillsell3desktopsonanygivenday”DesktopsSold#ofDaysDesktopsSold011/30=.03122/30=.0721010/30=.3331212/30=.40455/30=.17∑=1.00Copyright©2009CengageLearning6.7SubjectiveApproach…“Inthesubjectiveapproachwedefineprobabilityasthedegreeofbeliefthatweholdintheoccurrenceofanevent”E.g.weatherforecasting’s“P.O.P.”“ProbabilityofPrecipitation”(orP.O.P.)isdefinedindifferentwaysbydifferentforecasters,butbasicallyit’sasubjectiveprobabilitybasedonpastobservationscombinedwithcurrentweatherconditions.POP60%–basedoncurrentconditions,thereisa60%chanceofrain(say).Copyright©2009CengageLearning6.8InterpretingProbability…Nomatterwhichmethodisusedtoassignprobabilitiesallwillbeinterpretedintherelativefrequencyapproach...
