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) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (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) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text: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) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and
P(4 works) = 0.87, and these events are mutually independent.
1
2
(a) Find the probability that the system works.
(b) Find the probability that component 1 works, given that the system works.
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