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?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
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 99.6% 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
Transcribed Image Text: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
steps

Step by step

Solved in 4 steps with 8 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON