Answered: Consider a system consisting of four…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 54P

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Consider a system consisting of four components, as pictured in the following diagram.

A path begins on the left side of the diagram then continues horizontally to the right before splitting into a lower and an upper path. The upper path continues horizontally to the right and passes through 2 boxes labeled "1" and "2." The lower path continues horizontally to the right and passes through 2 boxes labeled "3" and "4." After passing through the boxes, the two paths rejoin and continue horizontally to the right before ending.

Components 1 and 2 form a series subsystem, as do Components 3 and 4. The two subsystems are connected in parallel. Suppose that

P(1 works) = 0.8

P(2 works) = 0.8

P(3 works) = 0.8

P(4 works) = 0.8

and that the four components work independently of one another.

(a)

Each subsystem only works if both components work, and the whole system will only work if at least one subsystem works. What is the probability of the system working if a 5–6 subsystem were added in parallel with the other two subsystems? (Round your answer to four decimal places.)

How does this probability compare to the probability of the system working if it only has the 1–2 and 3–4 subsystems?

The probability of the system with the 5–6 subsystem working is (HIgher/lower) than the probability of the system without the 5–6 subsystem working.

(b)

What is the probability of the system working if there were three components in series in each of the two subsystems? (Round your answer to four decimal places.)

The probability of the system with three components in each subsystem working is (Higher or Lower) than the probability of the system with two components in each subsystem working.

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