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What is the probability that all three components function properly throughout the warranty period?   (b) What is the probability that at least one component needs service during the warranty period?   (c) What is the probability that all three components need service during the warranty period?

What is the probability that all three components function properly throughout the warranty period?   (b) What is the probability that at least one component needs service during the warranty period?   (c) What is the probability that all three components need service during the warranty period?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...
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Question
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let 
A1
 be the event that the receiver functions properly throughout the warranty period, 
A2
 be the event that the speakers function properly throughout the warranty period, and 
A3
 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with 
P(A1) = 0.93,
 
P(A2) = 0.92,
 and 
P(A3) = 0.70.
 (Round your answers to four decimal places.)
(a)
What is the probability that all three components function properly throughout the warranty period?
 
(b)
What is the probability that at least one component needs service during the warranty period?
 
(c)
What is the probability that all three components need service during the warranty period?
 
(d)
What is the probability that only the receiver needs service during the warranty period?
 
(e)
What is the probability that exactly one of the three components needs service during the warranty period?
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