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 0.031 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.)

Factories A, B and C produce computers. Factory A produces 4 times as many computers as factory C, and factory B produces 6 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.013, the probability that a computer produced by factory B is defective is 0.049, and the probability that a computer produced by factory C is defective is 0.056. A computer is selected at random and it is found to be defective. What is the probability it came from factory A? Answer:

Testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests​ negative, then bothsamples are negative. On the other​ hand, one positive sample will always test​ positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.1​,find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?       ​(Round to three decimal places as​ needed.) Is the probability low enough so that further testing of the individual samples is rarely​ necessary?     A. The probability is​ low, so further testing will be necessary for all of the combined mixtures.   B. The probability is​ low, so further testing of the individual samples will be a rarely necessary event.   C. The probability is not​ low, so further…

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.)