Problem #2: Consider purchasing a system of audio components consisting of a rec

Question

Problem #2: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let Aj be the event that the receiver functions properly throughout the warranty period. Let A2 be the event that the speakers function properly throughout the warranty period. Let A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with PL41) 0.97, PL42) = 0.85, and P(A3) = 0.78. (a) What is the probability that at least one component needs service during the warranty period? (b) What is the probability that exactly one of the components needs service during the warranty period? Problem #2(a): Problem #2(b):

Explanation / Answer

Answer below:

a. P( atleast one component needs service during w.period)

= 1-P(no component needs service during w.period)

= 1-(.97*.85*.78)

= .35689

b. P( exactly oneof the components needs service during w.period)

= P(receiver ok)*P(speaker ok)*P(cd player not ok) + P(receiver ok)*P(speaker not ok)*P(cd player ok) +P(receiver not ok)*P(speaker ok)*P(cd player ok)

= (.97*.85*(1-.78))+(.97*(1-.85)*.78)+((1-.97)*.85*.78))

= .31477

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