5. 5.88 points DevoreStat9 2.E.084 My Notes Ask Your Teacher Consider purchasing

Question

5. 5.88 points DevoreStat9 2.E.084 My Notes Ask Your Teacher 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(A1)=0.98, P(A2)=0.91, and PAy) 0.80. (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? (e) 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? Need Help?eadTaik to a Tutor

Explanation / Answer

a) P(three components working properly) = 0.98 * 0.91 * 0.8 = 0.71344

b) P(at least one component need service during warrenty period) = 0.02 * 0.91 * 0.8 + 0.09 * 0.98 * 0.8 + 0.2 * 0.98 * 0.91 + 0.02 * 0.09 * 0.8 + 0.09 * 0.2 * 0.98 * 0.02 * 0.2 * 0.91 + 0.02 * 0.09 * 0.2 = 0.265

c) P(all three components need servicing) = 0.02 * 0.09 * 0.2 = 0.00036

d) P(only the receiver needs servicing) = 0.01456

e) P(exactly one component need servicing) = 0.02 * 0.91 * 0.8 + 0.09 * 0.98 * 0.8 + 0.2 * 0.98 * 0.91 = 0.26348

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