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### 13 Cards in this Set

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 PROBABILITY The mathematical model of chance phenomena concerned with random outcomes SAMPLE SPACE The set of all possible outcomes corresponding to an experiment, denoted by the Greek letter Omega. EVENT A particular subset of Omega, denoted by a capital letter. The components of the event are listed in brackets. UNION The union of two events A and B is event C, where either A or B or A and B could occur. Denoted by C=A U B. INTERSECTION The intersection of two events A and B is event C, where A and B both occur. Denoted by C=A n B. COMPLEMENT The complement is the event that A does not occur, or all elements in the sample space not in A. Denoted by Acomplement. EMPTY SET An empty set is a set with no elements, denoted by 0 with a line through it. DISJOINT If two or more events have no elements in common, they are disjoint. COMMUTATIVE LAW OF SET THEORY A U B = B U A A n B = B n A ASSOCIATIVE LAW OF SET THEORY (A U B) U C = A U (B U C) (A n B) n C = A n (B n C) DISTRIBUTIVE LAW OF SET THEORY (A U B) n C = (A n C) U (B n C) (A n B) U C = (A U C) n (B U C) PROBABILITY MEASURE A probability measure on Omega is a function P from subsets of Omega to the real numbers that satisfies: 1. P(Omega) = 1 2. If A < Omega, then P(A) >= 0 (no negative probability) 3. If A1 and A2 are disjoint, then P(A1 U A2) = P(A1) + P(A2) PROPERTIES OF PROBABILITY MEASURES Property A: P(Acomplement) = 1 - P(A) Proof: Because A and Acomplement are disjoin, P(A U Acomplement) = P(A) + P(Acomplement); also, A U Acomplement = Omega and P(Omega) - P(A U Acomplement) = 1 therefore 1 = P(A) + P(Acomplement), or P(Acomplement) = 1 - P(A) Property B: P(empty set) = 0 Property C: If A < B, then P(A) <= P(B) Property D: P(A U B) = P(A) + P(B) - P(A n B)