Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A, be the event that the receiver functions properly throughout the warranty period, A, be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A,) = 0.94, P(A,) = 0.97, and P(A,) = 0.90. (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?

Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A, be the event that the receiver functions properly throughout the warranty period, A, be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A,) = 0.94, P(A,) = 0.97, and P(A,) = 0.90. (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?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (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…
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