Transcription of Some Simple Counting Rules - Hamilton Institute
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Some Simple Counting Rules - Hamilton Institute
some Simple Counting RulesEE304 - Probability and StatisticsSemester 1 some Simple Counting RulesCountingIf all outcomes are equally likely, the probability of an eventEisgiven by|E||S|where|E|(|S|) denotes the number of elements inE(S).To apply this rule, we need to be able to count the number ofelements in events. We shall look at:Multiplication Rules ;Permutations of distinct objects;Permutations where some objects are identical;Combinations . some Simple Counting RulesSome Simple Counting RulesMultiplication Rule Basic ideaIf one operation can be done inn1ways and a second operationcan be done inn2ways then the number of different ways of doingboth we roll a fair die and toss a coin, the total number ofpossible outcomes is 6 2 = we roll a fair 4-sided die 3 times, the total number ofpossible outcomes is 4 4 4 = Simple Counting RulesSome Simple Counting RulesMultiplication Rule Basic ideaIf
Some Simple Counting Rules Multiplication RuleBasic idea If one operation can be done in n 1 ways and a second operation can be done in n 2 ways then the number of di erent ways of doing
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