Question

A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminates - organic pollutants, volatile solvents, and chlorinated compounds - 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 99.92% accuracy, and chlorinated compounds 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) Whatis the probability that the test will signal?

(b) Ifthe test signals, what is the probability that chlorinatedcompounds are present?

Answer 1

Explanation:

levels of organic pollutants with 99.7% accuracy

levels of volatile solvents with 99.92% accuracy

levels of chlorinated compounds with 89.7% accuracy

samples:

60% contaminated with organic pollutants

27% contaminated with volatile solvents

13% contaminated with traces of chlorinated compounds

a) probability that the test will signal?

P = 0.997*0.6 + 0.9992*0.27 + 0.897*0.13 = 0.5982 + 0.269784 + 0.11661 = 0.984594 = 98.45%

b) If the test signals, the probability that chlorinated compounds are present?

P = 0.897*0.13/0.984594 = 0.11661/0.984594 = 0.1184346035 = 11.84%