(4) 4. A new analytical method to detect pollutants in water is being tested. Th
ID: 3069593 • Letter: #
Question
(4) 4. A new analytical method to detect pollutants in water is being tested. The makers of the test claim that it can detect high levels of organic pollutants with .94 accuracy, volatile solvents with .90 accuracy, and chlorinated compounds If pollutant is not present, the test does not signal. Samples are prepared for calibration of the test and 40% of them are contaminated with organic pollutants, 35 % with volatile solvents, and 25 % with traces of chlorinated compounds. A test sample is selected at random with .85 accuracy Use Notation A1, A2, A3, B {test signals). ( a) What is the probability that the test will signal. 135 a5 b) If the test signals, what is the probability that organic pollutants are not present. RAB)Explanation / Answer
a) P(test will signal), P(B) = P(A1 and B) + P(A2 and B) + P(A3 and B)
= 0.40x0.94 + 0.35x0.90 + 0.25x0.85
= 0.9035
b) P(A1' | B) = P(A2 | B) + P(A3 | B)
= (0.35x0.90 + 0.25x0.85)/0.9035
= 0.5838
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