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Unformatted text preview: deﬁnition, we
need one more notion: two events are disjoint if their intersection is the empty
set, ;. A and B are not disjoint, but if C = {5, 6}, then A and C are disjoint.
207 208 APPENDIX A. REVIEW OF PROBABILITY A probability is a way of assigning numbers to events that satisﬁes:
(i) For any event A, 0 P (A) 1. (ii) If ⌦ is the sample space, then P (⌦) = 1.
(iii) For a ﬁnite or inﬁnite sequence of disjoint events P ([i Ai ) = P i P (Ai ). In words, the probability of a union of disjoint events is the sum of the probabilities of the sets. We leave the index set unspeciﬁed since it might be ﬁnite,
P ([k=1 Ai )
i = k
X P (Ai ) i=1 P1
or it might be inﬁnite, P ([1 Ai ) = i=1 P (Ai ).
i=1
In Examples A.1 and A.2, all outcomes have the same probability, so
P (A) = A/⌦
where B  is short for the number of points in B . For a very general example of a
P
probability, let ⌦ = {1, 2, . . . , n}; let pi 0 with i pi = 1; and deﬁne P (A) =
P
i2A pi . Two basic properties that follow immediatel...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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