Switches 1 & 2 are in series.
So,
P(Switches 1 & 2 together working) = p1 p2
Switches 3 & 4 are in series.
So,
P(Switches 3 & 4 together working) = p3 p4
Switches 1&2 and 3 & 4 are in parallel.
So,
P(Switches 1 & 2 and 3 & 4 together working) = 1 - {(1-p1 p2) (1 - p3 p4)}
Switches 1&2 and 3&4 and Switch 5 are in series.
So,
Probability that the system works is given by:
[1-{( 1 - p1 p2) (1 - p3 p4)}] p5
A system with four switches is shown below. The probability that any of the switches operate...
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