BasicProbability
AssessingProbability
• Probability:chance/likelihoodthatanuncertaineventwilloccur.
• Impossibleevent=0;certainevent=1.
• Event:eachpossibleoutcomeofavariable.
o Simpleevent–singlecharacteristic.
o Jointevent–twoormorecharacteristics.
o ComplementofaneventA(A’)–alleventsnotpartofA(1-P(A)).
• SampleSpace:collectionofallpossibleevents.
• Mutuallyexclusiveevents:cannotoccursimultaneously.
• Collectivelyexhaustiveevents:oneoftheeventsinthesamplespacemust
occur.
• Approaches:
1. Apriori:basedonpriorknowledgeoftheprocess
2. Empirical:basedonobserveddata(experimentalprobability)
o empiricalprobabilityofjointevent:
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3. SubjectiveProbability:basedonanindividual’spastexperience,
personalopinionand/oranalysisofasituation.
GeneralAdditionRule:
o Addtogethermarginalprobabilityofmutuallyexclusiveevents
ConditionalProbability:probabilityofoneevent,giventhatanothereventhas
occurred.
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Independence:2eventsareindependentonlyif…
o Independentwhenprobabilityofoneeventis
noteffectedbyanotherevent.
o Conditionalprobabiltiyunchangedfrommarginalprobability.
Multiplicationrule:
BayesTheorem
• Usedtoreviseexistingprobabilities
(marginal)withnewinformation.
• Extensionofconditionalprobability–
reverseconditioningbetweentwo
events.
• Marginal
Probability: