7-2 - 7-2 Union, Complement of Events, OddsTHEOR(UNION)...

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Unformatted text preview: 7-2 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(E1E2) = + - = 7-2p. 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 Econsume 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) 7-2p. 2 HTTHHHTTEEODDS...
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7-2 - 7-2 Union, Complement of Events, OddsTHEOR(UNION)...

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