1)

I Consider the system of components connected as in the gure below. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either i or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(l works) = 0.7V}, P(2 works) = 0.?3, P(3 works) = 0.8, and PM works) = 0.89. Find the probability that the system works. I Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A1 be the event that the receiver functions properly throughout the warranty period. Let .42 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(A1) = 0.96, P(A2) = 0.88, and P(A3) = 0.74. (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