Question A system contains three components A B and C connec

Question: A system contains three components, A, B, and C, connected in series, as shown below in the diagram:

(a) If the probability that A fails is 0.06, the probability that B fails is 0.04, and the probability that C fails is 0.05, find the probability that the system functions.

(b) If both A, B, and C have probability p of failing, what must be the value of p so that the probability that the system functions is 0.90?

Solution

For the system to function All A, B and C must funciton

a) Prob that the system functions = P(ABC)

= 0.94(0.96)(0.95)

= 0.857280

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b) P(ABC) = (1-p)³ =0.90

1-p = 0.9655

p = 1-0.9655

= 0.0345