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) = 0.77, P(2 works) = 0.79, P(3 works) = 0.84, andP(4 works) = 0.84, and these events are mutually independent.312(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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Answered: Consider the system of independent…

A First Course in Probability (10th Edition)

10th Edition

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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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Oo.121. Subject :- Advance Mathematic
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1.9
If æ(0) 3x1 – x2 = 7 -21 + 4x2 = 8 0, then æ(1) in the Gauss-Seidel iteration of the following system is a. O b. 59/12 7 39/4 d. 7/3 [ 31/12 е. Of. 3. g. Oh. 7 15/4. O i. 0 O j. 13/3
Suppose the system to the right is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. Select the correct answer below. O A. Since f and g are arbitrary, c and d can be any value and the system will be consistent. O B. O D. yamnle The row reduction of 1 11 [ C dg arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an equation of bx₂=0 where b is nonzero. Thus, c=d=0. The row reduction of to Taythank HITS 1 11 f OC. Since f and g are arbitrary and the system is consistent for all possible values of f and g, c = 0 and d = 1. Otherwise, the triangular form of the matrix will show that the system is inconsistent. 1 11 0 d-11c g-cf to f 1 [ shows that d-11c #0 since f and g are arbitrary C dg Otherwise, for some choices off and g, the second row could correspond to an equation of 0=b, where b is nonzero. Thus, d# 11c. X₁ + 11x₂=f CX₁ + dx₂=g shows that d-11c=0 since f and g are 11 f 0 d-11c…

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