   Chapter 9.9, Problem 4ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# a. Prove that if A and B are any events in a sample space S, with P ( B ) ≠ 0 , then P ( A c | B ) = 1 − P ( A | B ) . b. Explain how the result in a part (a) justifies the following statements: (1) If the probability of a following statements: (1) If the probability of a false positive on a test for a condition is 4%, then there is a 96% probability that a person who does not have the condition will have a negative test result. (2) If the probability of a false negative on a test for a condition is 1%, then there is a 99% probability that a person who does have the condition will test positive for it.

To determine

To prove that P(Ac|B)=1P(A|B).

Explanation

Given information:

A and B are events in sample space S and P(B)0.

Calculation:

P(Ac|B)=P(AcB)P(B)=P(BA)P(B)=P(B)P(AB)P

To determine

To explain how the result in part (a) justifies the following statements.

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