4. A system contains four components, connected as shown in the diagram Treat co

Question

4. A system contains four components, connected as shown in the diagram Treat components A and B as Sub-system 1. Treat components C and D as Sub-system 2. Suppose the components and sub-systems i A, 0.02 for B, 0.05 for C, and 0.03 for D. tems function independently, and that the probabilities of failure are 0.01 for Find the probability of success for each of the four components (A, B, C, D). You only need to show the formula and your work once for P(A). (5 pts) P(A) a) P(B) P(C) P(D) b) Find the probability that Sub-system 1 succeeds, P(SS,). (3 pts) c) Find the probability that Sub-system 2 succeeds, P(SS2). (3 pts) d) Find the probability that the overall system succeeds, P(SSo). (3 pts) 14

Explanation / Answer

a) P(A) =1-0.01 =0.99

P(B) =1-0.02 =0.98

P(C) =0.95

P(D) =0.97

b)P(SS1) =1-P(neither A nor B works) =1-0.01*0.02=0.9998

c) P(SS2) =1-P(neither C nor D ) works =1-0.05*0.03=0.9985

d)probability that overall system succeds =1-P(none of SS1 and SS2 works) =1-(1-0.9998)*(1-0.9985)

=0.9999997

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