# probability that the circuit operates

This electrical circuit operates if and only if there is a path of the functional devices from left to right. The probability that each device functions is as shown. 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?

0.9--------0.8--------0.7--------

-------/

------------------

0.95-----0.95-------0.95-------/

Drawn poorly, but the current comes in from the left, flows through the top, bottom or both, and leaves at the right.

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#### Solution Preview

All three devices have to function for that branch functions.

The probability of the upper branch functioning is

0.9 * 0.8 * 0.7 = 0.504

The ...

#### Solution Summary

The solution shows how to calculate the probability the electric circuit operates.