Consider purchasing a system of audio components consisting of a receiver, a pai
ID: 3277445 • Letter: C
Question
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, 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 PIA)-0.96, P(A2)-0.94, and 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?Explanation / Answer
Answers to all parts here:
a.
P( all components function ) = P(A1 and A2 and A3 function properly) = .96*.94*.70 = .6317
b.
P( atleast 1 component needs serive)
= 1-P( not component need service)
= 1- P( all are good)
= 1-.96*.94*.70
0.3783
c.
P(all 3 need service)
= P( each doens't func. properly)
= P(A1 doesn't func prop)*P(A2 doesn't func prop)*P(A3 doesn't func prop)
= (1-.96)(1-.94)(1-.70)
= 0.00072
d.
P( only reciver needs service)
= P( A1 is not function properly)*P( A2 is good )*P(A3 is good)
= (1-.96)*.94*.70
= 0.0263
e.
P(only 1 needs service)
= P(only A1 needs, A2 and A3 are fine)+P(only A2 needs, A1 and A3 are fine)+P(only A3 needs, A2 and A1 are fine)
= (1-.96)*.94*.70 + (1-.94)*.96*.70 +.96*.94*(1-.70 )
= 0.3374
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