Consider a sample space S that has N mutually exclusive events B, n=1,2,...,N , such that BB, = {Ø} for m+n=1,2..N. The probability of any event A, defined on this sample space can be expressed in terms of the conditional probabilities of events B„ This probabili is known as the total probability of event A. Mathematically, n' N P)-ΣΡΑ| Β.)PB ) n-1

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 5SE: The union of two sets is defined as a set of elements that are present in at least one of the sets....
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Prove the property

Consider a sample space S that has N mutually exclusive events B, n=1,2,..,N , such that
‚N,such that
%3D
Bm B, = {0} for m#n=1,2....N. The probability of any event A, defined on this sample
space can be expressed in terms of the conditional probabilities of events B „.This probability
is known as the total probability of event A.
Mathematically,
P(A) = P(A\B,)P(B,)
(1
n=1
Transcribed Image Text:Consider a sample space S that has N mutually exclusive events B, n=1,2,..,N , such that ‚N,such that %3D Bm B, = {0} for m#n=1,2....N. The probability of any event A, defined on this sample space can be expressed in terms of the conditional probabilities of events B „.This probability is known as the total probability of event A. Mathematically, P(A) = P(A\B,)P(B,) (1 n=1
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