A system consists of four components, connected as shown in the diagram. Suppose that the components function independently, and that the probabilities of failure are 0.05 for
A. 0.05
B. 0.03
C. 0.07
D. 0.14
Find the probability that the system functions.
P(system functions) = P[(A ? B) ? (C 
D)]. Now P(A ? B) = P(A)P(B) = (1?0.05)(1 ? 0.03) = 0.9215, and P(C D) = P(C) + P(D) ? P(C ? D) = (1?0.07) + (1 ? 0.14) ? (1 ? 0.07)(1 ? 0.14) = 0.9902.
Therefore
P[(A ? B) ? (C D)]=P(A ? B)P(C D)
=(0.9215)(0.9902)
=0.9125
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