To assure safety, a mechanical system hasthree components: the main machine and 2backup machines. The system fails only if allthese components fail. Assuming that thesecomponents function independently, computefor the probability that the system fails giventhe following information:*P(main machine fails) = 0.1*P(1st back-up machine fails) = 0.05*P(2nd back-up machine fails) = 0.025%3DSelect the correct response:O 1.25 x 10^-4none of theseO 0.005O 0.00125

It is given that P(main machine fails) = 0.1 P(1st back-up machine fails) = 0.05 P(2nd back-up…

Answered: To assure safety, a mechanical system…

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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In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.037 and the system that utilizes the component is part of a triple modular redundancy. (a) What is the probability that the system does not fail? (b) Engineers decide to the probability of failure is too high for this system. Use trial and error to determine the minimum number of components that should be included in the system to result in a system that has greater than a 0.99999999 probability of not failing. (a) The probability is. (Round to eight decimal places as needed.)

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