The source is given sample suggestions for probability, and its equivalent in conditional probability has been defined.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 40E
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The source is given sample suggestions for probability, and its equivalent in conditional probability has been defined.

Prove the conditional rule.

Rule
Conditional rule
Probability axiom
completion rule
0< P(E) < 1
P(E) = 1 – P(E“)
P(EF) = P(E|F)P(F)
0 < P(E\G) <1
P(E|G) = 1 – P(E°\G)
P(EF|G) = P(E|FG)P(F|G)
Chain Rule
%3D
%3D
Transcribed Image Text:Rule Conditional rule Probability axiom completion rule 0< P(E) < 1 P(E) = 1 – P(E“) P(EF) = P(E|F)P(F) 0 < P(E\G) <1 P(E|G) = 1 – P(E°\G) P(EF|G) = P(E|FG)P(F|G) Chain Rule %3D %3D
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