The circuit above operates if and only is there is a path of

The circuit above operates if and only is there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that the probability that a device is functional does not depend on whether or not other devices are functional. What is the probability that the circuit operates?

Solution

For each part of this loop, the probability that it functions is 1 minus the probability that both elements fail:

Pr(loop 1) = 1 (1 0.9)(1 0.95) = 0.995 Pr(loop 2) = 1 (1 0.9)(1 0.95) = 0.995 Pr(loop3) = 1(10.8)(10.9)=0.98

P r(circuit functions) = P r(loop 1)P r(loop 2)P r(loop 3) = 0.995 × 0.995 × 0.98 = 0.97021