Question

Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. 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. Suppose that P(1 works) = 0.78, P(2 works) = 0.77, P(3 works) = 0.86, and P(4 works) = 0.85. (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.

          Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. 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. Suppose that P(1 works) = 0.78, P(2 works) = 0.77, P(3 works) = 0.86, and P(4 works) = 0.85.
(a) Find the probability that the system works.
(b) Find the probability that component 1 works, given that the system works.

Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. 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. Suppose that P(1 works) = 0.78, P(2 works) = 0.77, P(3 works) = 0.86, and P(4 works) = 0.85.
(a) Find the probability that the system works.
(b) Find the probability that component 1 works, given that the system works.

Added by Jaime S.

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