Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another and P(component i works) = 0.82 for i = 1, 2 and = 0.69 for i = 3, 4, calculate P(system works). (Round your answer to four decimal places.)
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another and P(component i works) = 0.82 for
and = 0.69 for
calculate P(system works). (Round your answer to four decimal places.)
The probability of working parallel components is the probability of the union of components.
The probability of the union of events and is as follows.
And the probability of working of a series of components is the probability of the intersection of components.
If the events are independent then their probability of intersection is as follows.
Given that,
Two components are and in parallel. It is subsystem
Two components are and in series. It is subsystem
The components are workers independently.
The probability of components works is given below.
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