QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
| 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 triple modular redundancy. | |
| --- | --- |
| (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 at least one of the components does not fail? | |
| (a) The probability is . | |
| (Round to eight decimal places as needed.) | |
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Step 1I'll solve this problem step by step using precise probability calculations and LaTeX formatting.
- Probability of a single component failing = $$p = 0.0052
Given: - Triple modular redundancy system
Step 2: Calculate the probability of a single component failing
- Probability of failure = $$p = 0.0052
- Probability of success = 1 - p = 0.9948
Final Answer
(a) Probability of all three components failing: 0.00000140608 (b) Probability of at least one component not failing: 0.99999859392
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