A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is importantbecause, if adopted, it could be used to detect three different contaminates - organic pollutants, volatile solvents, andchlorinated compounds - instead of having to use a single test for each pollutant. The makers of the test claim that it candetect high levels of organic pollutants with 99.6% accuracy, volatile solvents with 99.91% accuracy, and chlorinatedcompounds with 89.4% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for thecalibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% withtraces 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 the chlorinated compounds are present?Carry out all calculations exactly, then round the final answers to four decimal places (e.g. 0.9876).(a) i(b) iStatistical Tablad Chand

Answered: A new analytical method to detect…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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 99.6% accuracy, volatile solvents with 99.91% accuracy, and chlorinated
compounds with 89.4% 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 the chlorinated compounds are present?
Carry out all calculations exactly, then round the final answers to four decimal places (e.g. 0.9876).
(a) i
(b) i
Statistical Tabla
d Chand

Expert Solution

Step 1: Given Information

Given that,
A new analytical method to detect pollutants in water is being tested.
The event A represents that test will signal.
The event $B subscript 1 comma space B subscript 2 comma space text and end text space B subscript 3$ represents that water is polluted with organic pollutants, volatile solvents and chlorinated compounds respectively.
i.e. $P open parentheses A over B subscript 1 close parentheses equals 99.6 percent sign space space space space space space space space space space space space space equals 0.996$
$P open parentheses A over B subscript 2 close parentheses equals 99.91 percent sign space space space space space space space space space space space space space equals 0.9991$
$P open parentheses A over B subscript 3 close parentheses equals 89.4 percent sign space space space space space space space space space space space space space equals 0.894$
$P open parentheses B subscript 1 close parentheses equals 0.60 P open parentheses B subscript 2 close parentheses equals 0.27 P open parentheses B subscript 3 close parentheses equals 0.13$

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