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Unformatted text preview: 72 Union, Complement of Events, OddsTHEOR(UNION) OFTWOEVENTSRandom experiment: flip coin twiceEvent 1: E1 = get head on first throw = {HH, HT}Event 2: E2 = get the same on both throws = {HH, TT}What is the probability of event E1 ORE2:head on the first throwORsame on both throwsS = Sample SpaceDefinition: E1 ORE2 = E1 ∪E2P(E1 ORE2) = P(E1 ∪E2) = )S(n)2E1E(n∪= )S(n)2E1n(E) 2n(E) 1n(E∪+= )S(n)2E1E(n)S(n)2E(n)S(n)1E(n)S(n)3E(n∩+== P(E1) + P(E2) – P(E1∩E2) = ½ + ½  ¼ = ¾ 72p. 1 HTTHE2HHTTE1P(A ORB)For any two events A and BP(A or B) = P(A ∪B) = P(A) + P(B) – P(A ∩B)If A and B are disjoint,P(A or B) = P(A ∪B) = P(A) + P(B)THENOT(COMPLEMENT) OFANEVENTRandom experiment: flip coin twiceEvent E: get head on first throw = {HH, HT}Event E′:NOTgetting a head on the first throwWhat is the probability of event E′?S = Sample SpaceSince E and E′consume the whole spaceP(E) + P(E′) = 1, and P(E′) = 1 – P(E)P(NOT A)For any event A P(not A) = P(A′) = 1  P(A) 72p. 2 HTTHHHTTEE′ODDS...
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 Spring '11
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 Probability, Probability theory

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