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 Ai 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 P(Ai)-0.99, P(A2) 0.87, and P(A3) 0.72. (a) What is the probability that at least one component needs service during the warranty period? tb) Whatis the probability that exactl the components needs service during the warranty period?

Explanation / Answer

a) P(Atleast one component needs service)

= 1 - P(None needs service)

= 1 - 0.99*0.87*0.72

= 0.379864

b) P(Exactly one of the components needs service)

= P(A needs service, B and C fine) + P(B needs service, A and C fine) + P(C needs service, A and B fine)

= (1-0.99)*0.87*0.72 + 0.99*(1-0.87)*0.72 + 0.99*0.87*(1-0.72)

= 0.340092

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