If the events B1, B2, ..., Br constitute a partition of the sample space S such that P(B;) #0 for i 1, 2,..., k, then for any event A of S, k k P(A) = P(B; n A) = P(Bi)P(A|B;). i=1 i=1
If the events B1, B2, ..., Br constitute a partition of the sample space S such that P(B;) #0 for i 1, 2,..., k, then for any event A of S, k k P(A) = P(B; n A) = P(Bi)P(A|B;). i=1 i=1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Transcribed Image Text:If the events B1, B2, . . , B, constitute a partition of the sample space S such that
P(B;) # 0 for i = 1, 2, ... , k, then for any event A of S,
%3D
k
k
P(A) = P(B;n A) =P(B;)P(A|B;).
%3D
i=1
i=1
B3
B1
B5
B4
B2
...
Figure 14: Partitioning the sample space S.
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