It states that if a sample space S has N mutually exclusive events B, n=1,2,....,N, such that, B, OB, = {0} for m +n = 1,2,.., N, and any event A is defined on this sample space then the conditional probability of B, and A can be written as P(A|B,) P(B,) PSA|B)P(B)+ P(A|B2)P(B,)+……+P(A|By)P(By) (1.5 P(B, | A) =

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 30CT: In a batch of 20 tires, 2 are known to be defective. If 4 tires are chosen at random, find the...
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Prove the property

It states that if a sample space S has N mutually exclusive events B,, n=1,2,....,N, such
that, Bm B,= {0} for m +n = 1,2,...., N, and any event A is defined on this sample space,
לn
•...
then the conditional probability of B, and A can be written as
Р(В, | А)
Р(4| В, ) Р(В,)
(1.55)
P(A|B)P(B,)+P(A|B,)P(B,)+………+P(A|By)P(B»)
..+
Transcribed Image Text:It states that if a sample space S has N mutually exclusive events B,, n=1,2,....,N, such that, Bm B,= {0} for m +n = 1,2,...., N, and any event A is defined on this sample space, לn •... then the conditional probability of B, and A can be written as Р(В, | А) Р(4| В, ) Р(В,) (1.55) P(A|B)P(B,)+P(A|B,)P(B,)+………+P(A|By)P(B») ..+
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