A new analytical method to detect pollutants in water is beingtested. This new m

Question

A new analytical method to detect pollutants in water is beingtested. 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. Themakers of the test claim that it can detect high levels of organicpollutants with 99.3% accuracy, volatile solvents with 99.92%accuracy, and chlorinated compounds with 89.7% accuracy. If apollutant is not present, the test does not signal. Samples areprepared for the calibration of the test and 60% of them arecontaminated with organic pollutants, 27% with volatile solvents,and 13% with traces of chlorinated compounds. A test sample isselected randomly.

(a) What is the probability that the test will signal?

(b) If the test signals, what is the probability that thechlorinated compounds are present?

Round your answers to four decimal places (e.g. 98.7654).

Explanation / Answer

(a) P(will signal) = 0.60 x 0.993 + 0.27 x 0.9992 + 0.13 x 0.897 =0.9822 (b) P(Chlorinated compounds|test signals)     = P(Chlorinated compunds and Testgignals)/P(Test signals)     = 0.11661/0.9822     = 0.1187 Hope this helps!

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