7. The following circuit operates if and only if there is a path of functional devices from left toright. The probability each device functions is as shown. Assume that the probability that adevice function does not depend on whether or not other devices are functional. What is theprobability that the circuit operates?0.90.90.80.950.950.98. A new analytical method to detect pollutants in water is being tested. This new method ofchemical analysis is important because, if adopted, it could be used to detect three differentcontaminants-organic pollutants, volatile solvents, and chlorinated compounds-instead ofhaving to use a single test for each pollutant. The makers of the test claim that it can detecthigh levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracyand chlorinated compounds with 89.7% accuracy. If a pollutant is not present, the test doesnot signal. Samples are prepared for the calibration of the test and 60% of them arecontaminated with organic pollutants, 27% with volatile solvents, and 13% with traces ofchlorinated compounds. A test sample is selected randomly.a. What is the probability that the test will signal?b. If the test signals, what is the probability that chlorinated compounds are present?

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Answered: 7. The following circuit operates if…

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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A company is introducing a new product into the market. If the sales are high, there is a 0.6 probability that they will remain so next month. If they are not, the probability that will become high next month is only 0.1. The company has the option of launching an advertisement campaign. If it does and the sales are high, the probability that they will remain high next month will increase to 0.7. On the other hand, an advertising campaign while the sales are low will raise the probability to only 0.3. If no advertisement is used and the sales are high, the returns (in thousands of dollars) are expected to be 9 if the sales remain high next month and 3 if they do not. The corresponding returns if the product starts with low sales are 6 and -3. Using advertisement will result in returns of 8 if the product starts with high sales and continues to be so and 5 if it does not. If the sales start low, the returns are 4 and -6, depending on whether or not they remain high. Compute the…
Events A and B of a probability space (Q,F,P) are independent. The probability that the both 3 and the probability that at least one event occurs is 25 17 . Determine P(A) occur is 25 and P(B).
A company is introducing a new product into the market. If the sales are high, there is a 0.6 probability that they will remain so next month. If they are not, the probability that will become high next month is only 0.1. The company has the option of launching an advertisement campaign. If it does and the sales are high, the probability that they will remain high next month will increase to 0.7. On the other hand, an advertising campaign while the sales are low will raise the probability to only 0.3. If no advertisement is used and the sales are high, the returns (in thousands of dollars) are expected to be 9 if the sales remain high next month and 3 if they do not. The corresponding returns if the product starts with low sales are 6 and -3. Using advertisement will result in returns of 8 if the product starts with high sales and continues to be so and 5 if it does not. If the sales start low, the returns are 4 and -6, depending on whether or not they remain high. Obtain the…
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