Assume A and B function independently. For the system to function, both components must function.
A system contains two components, A and B, connected in series, as shown in the diagram.
a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, find the probability that the system functions.
b. If both A and B have probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?
c. If three components are connected in series, and each has probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?
a) P(A ? B) = P(A)P(B) = (1?0.05)(1 ? 0.03) = 0.9215
(b) P(A ? B) = 
= 0.9. Therefore p = 1 - 
= 0.0513.
(c) P(three components all function) = 
= 0.90. Therefore p = 
= 0.0345.
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