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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)