10. (a) In order that the system S1 consisting of components A and B should func

Question

10. (a) In order that the system S1 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 functions, given that A. B have probabilities 08, 09 respectively of functioning correctly (b) The system is connected in parallel in such a way that if either of the sub-systems A-B functions correctly. S, functions correctly. Find the probability that S, functions correctly. (c) The system functions correctly if either A and either B function correctly. Find the probability that S, functions correctly

Explanation / Answer

a) probability that S1 function = P(A and B)
= P(A) * P(B)
= 0.8 *0.9
= 0.72

b)
probability that S2 function
X1 = upper line works
X2= lower line works
P(X1) = 0.72 = P(X2)
hence P(X1) + P(X2) - P(X1 and X2)
= 0.72 +0.72 - 0.72*0.72
= 0.9216

c)
X1 = at least one of A works
X2 = at least one of B works
P(X1) = 1 - (1-p)^2
= 1 - (1-0.8)^2 = 0.96
P(X2) = 1 - (1-0.9)^2 =0.99

hence P(X1 and X2)
= 0.96 *0.99
=0.9504

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