Question: A system consists of five components in two branches as shown in the f

Question

Question: A system consists of five components in two branches as shown in the following diagram: For the s... A system consists of five components in two branches as shown in the following diagram:
For the system to work, A must work with B, or C,D,E must work together.
In other words, the system works if components A and B work or components C, D, andE work. Assume that the components fail independently with the following probabilities:
P(A fails) = P(B fails) = 0.3 and P(C fails) = P(D fails) = P(E fails) = 0.2.
(a) What is the probability that the system works?
(b) Given that the system works, what is the probability that component A does not work?
(c) Given the system does not work, what is the probability that component A also does not work? --B ds, the system works if components A and B work or com

Explanation / Answer

a) P(A and B works) = 0.7x0.7 = 0.49

P(C, D and E works) = 0.8x0.8x0.8 = 0.512

P(system works) = P(A or B fails) x P(C,D or E fails)

= (1 - 0.49) x (1 - 0.512)

= 0.249

b) P(A does not work | system works) = P(A does not work and system works) / P(system works)

= (0.3x1 x 0.512)/0.249

= 0.617

c) P(A does not work | system doest not works) = P(A does not work and system doest not work) / P(system does not work)

= [0.3x1 x (1-0.512)]/[1 - 0.249]

= 0.195

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