A new analytical method to detect pollutants (D) in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants-organic pollutants (O), volatile solvents (V), and chlorinated compounds (C)-instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated components with 89.7% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated 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? Note: Use the notations in the brackets to describe the events.
A new analytical method to detect pollutants (D) in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants-organic pollutants (O), volatile solvents (V), and chlorinated compounds (C)-instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated components with 89.7% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated 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? Note: Use the notations in the brackets to describe the events.
Biomedical Instrumentation Systems
1st Edition
ISBN:9781133478294
Author:Chatterjee
Publisher:Chatterjee
Chapter5: Biomedical Electronics: Digital
Section: Chapter Questions
Problem 5Q
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A new analytical method to detect pollutants (D) in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants-organic pollutants (O), volatile solvents (V), and chlorinated compounds (C)-instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated components with 89.7% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated 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?
Note: Use the notations in the brackets to describe the events.
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