   Chapter 9.9, Problem 10ES ### 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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# Prove the full version of Bayes’ theorem.

To determine

To prove the full version Bayes’ theorem.

Explanation

Given information:

A sample space S is a union of mutually disjoint events A1A2A3.....An, such that P(Ai)>0 for i=1,2,3.... if E is an event in S with P(E)>0, then

P(Ak|E)=P(Ak)P(E|Ak)i=1nP(Ai)P(E|Ai) for k=1,2,3....

Calculation:

It is given that S is a union ofmutually disjoint events A1A2A3.....An.

S=A1A2A3.....AnE=ESE=E(A1A2A3.....An)E=(EA1)(EA2)....(EAn){since E is any event is S therefore  <

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