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13 Cards in this Set
 Front
 Back
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) 