Consider purchasing a system of audio components consisting of a receiver, a pai

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 A be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A) = 0.98, P(A2-0.91, and P() = 0.80. (Round your answers to four decimal places.) (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

Solution:-
(a) The probability that all three components function properly through the warranty period : 0.7134

=> P(A1)*P(A2)*P(A3) = 0.98*0.91*0.80 = 0.7134

(b) The probability that at least one component needs service during the warranty period = 0.2866

=> 1 - 0.7134 = 0.2866

(c) The probability that all three components need service during the warranty period is 0.0004

=> (1-P(A1))*(1-P(A2))*(1-P(A3)) = 0.02*0.09*0.20 = 0.00036 = 0.0004

(d) The probability that only the receiver needs service during the warranty period is 0.0146

=> P(A1-Bar)*P(A2)*P(A3) = 0.02*0.91*0.80 = 0.01456 = 0.0146

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