Consider the system of independent components connected as in the figure below. The system works only if thereis a path of functional components from left to right. Components 1 and 2 are connected in parallel, so thatsubsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works ifand only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, andP(4 works) = 0.87, and these events are mutually independent.12(a) Find the probability that the system works.(b) Find the probability that component 1 works, given that the system works.

Answered: Image /qna-images/answer/32613c19-4e19-414c-95e5-3cac867a90cc.jpg

Answered: Consider the system of independent…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3x3 = 1 -2x1 + x2 – X3 = 2 X1 — Зх2 + 6х3 = 3 X1 Let x be the vector x = x,, where x1, x2 and x3 are solutions of the system, and y be the vector y = 1|. Evaluate the (X3) scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.]
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