In order that the system consisting of components A and B should function correc

Question

In order that the system consisting of components A and B should function correctly, both components must function correctly. Assuming that each component functions independently of the other, find the probability that S_1 functions, given that A, B have probabilities 0.8, 0.9 respectively of functioning correctly. The system is connected in parallel in such a way that if either of the sub-systems A-B functions correctly, S_2 functions correctly. Find the probability that S_2 functions correctly. The system functions correctly if either A and either B function correctly. Find the probability that S_3 functions correctly.

Explanation / Answer

S1->P(Work)=0.9*0.8=0.72

S2->P(Work)=0.72+0.72-0.72*0.72=0.9216

S3->P(Work)=(0.8+0.8-0.8*0.8)(0.9+0.9-0.9*0.9)=0.9504

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