   Chapter 9.8, Problem 13ES ### 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
1 views

# Use the axioms for probability and mathematical induction to prove that for each integer n ≥ 2 , if A 1 , A 2 , A 3 , .... A n are any mutually disjoint events in a sample space S, then   P ( A 1 ∪ A 2 ∪ A 3 ∪ ... ∪ A n ) = ∑ k = 1 n P ( A k ) .

To determine

Proof of the given statement.

Explanation

Given information:

A sample space S and for each integer n2, if A1,A2,A3.....,An are mutually disjoint events then, P(A1A2A3...An)=k=1nP(Ak).

Calculation:

Since, above events are mutually disjoint sets,

P(A1A2A3...Ak)Ak+1=

And A1A2A3...AkAk+1=(A1A2A3

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