Question 1. The apparatuses of a “6-component system” are to be randomly chosen from a box of 20 used apparatuses. The resulting system will be functional if at least 4 of its 6 apparatuses are in working circumstances. If 5 of the 20 components in the box are not in working circumstances, what is the probability that the resulting system will be a nonfunctional ?

Question 1. The apparatuses of a “6-component system” are to be randomly chosen from a box of 20 used apparatuses. The resulting system will be functional if at least 4 of its 6 apparatuses are in working circumstances. If 5 of the 20 components in the box are not in working circumstances, what is the probability that the resulting system will be a nonfunctional ?

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 0.0052 and the system that utilizes the component is part of (a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight? (b) What is the probability triple modular redundancy. least one of the components does not fail? (a) The probability is. (Round to eight decimal places as needed.)
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
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A company manufacturing CDs is working on a new technology. A random sample of 646 Internet users were asked: "As you may know, some CDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with this technology, or would you refuse to buy it even if it was one you would normally buy?" Of these users, 59% responded that they would buy the CD. Complete parts a and b below. a) Create a 99% confidence interval for this percentage. ( 54.008 %, 63.993 %) (Round to three decimal places as needed. Use ascending order.) b) If the company wants to cut the margin of error by two thirds, how many users must they survey? The company must survey a total of (Type a whole number.) users
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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 0.039 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 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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Valve A: 92% Valve B: 94% Valve C: 93%
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.)