Probability_week_3 - Probability Conditional probability...

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ProbabilityConditional probabilityIndependenceComplementary eventsAdditive ruleMultiplicative rule
Conditional probabilityWhen the occurrence of one event alters the probability ofoccurrence of another event, these events aredependent.Theconditional event AgivenBis indicated by (A/B) andreads as “event A given B”EXAMPLE:A set of 15 marbles contains 4 red and 11 greenmarbles.If two marbles are taken from this set one at a time,andwithout replacementa)What is the probability that the first marble selected is red?b)What is the probability that the second marble is red giventhat the first marble is red?
Conditional probabilityEXAMPLE:Thecontingency tablebelow provides an example of400 parts classified by surface flaws and as (functionally)defectivea)What is the probability of a defective part assuming that thepart has surface flaws?Surface flawsDefectiveYesNoTotalYes101828No30342372Total40360400
Conditional probabilityIf A and B are any two events, then the conditionalprobability of A given B, denoted by,is,providedWith the event ,

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