Determine P[(A Union B Union C)\']. The following circuit operates if and only i

Question

Determine P[(A Union B Union C)']. The following circuit operates if and only if there is a path of 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 does not depend on whether or not other devices are functional. What is the probability that the circuit operates? (The answer in the back of the book is incorrect.) Let X denote the number of bars of service on your cell phone whenever you are at an intersection with the following probabilities:

Explanation / Answer

Device with probability 0.9 & Device with probability 0.8 are in series.

So, the probability of operation of these 2 devices in Series = 0.9 X 0.8 = 0.72

The 2 devices with 0.95 are in series.

So, the probability of operation of these 2 devices in Series = 0.95 X 0.95 = 0.9025

Now:
We have 2 sets of devices with probability 0.72 & 0.9025 and they are in prallel,

So, the probability that the circuit operates is

=1 - [ (1-0.72) X (1 - 0.9025]

= 1 - [ 0.28 X 0.0975 ]

= 1 - 0.0273

= 0.9727

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