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For any two events A and B with P(B) > 0, prove that P (AC |B) = 1 - P(A/B)

For any two events A and B with P(B) > 0, prove that P (AC |B) = 1 - P(A/B)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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For any two events A and B with P(B) > 0, prove that P (Aº | B) = 1 - P(A/B)
Transcribed Image Text:For any two events A and B with P(B) > 0, prove that P (Aº | B) = 1 - P(A/B)
Expert Solution
Step 1: Introduce the given information

Given two events A and B with P(B) > 0.

Using formulas,

1 right parenthesis space P left parenthesis X vertical line Y right parenthesis equals fraction numerator P left parenthesis X intersection Y right parenthesis over denominator P left parenthesis Y right parenthesis end fraction

2 right parenthesis space P left parenthesis X intersection Y right parenthesis equals P left parenthesis Y intersection X right parenthesis

3 right parenthesis space P left parenthesis X intersection Y to the power of c right parenthesis equals P left parenthesis X right parenthesis minus P left parenthesis X intersection Y right parenthesis

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