A new analytical method used to detect pollutants is beingtested. The makers of

Question

A new analytical method used to detect pollutants is beingtested. The makers of the test claim that it can detect highlevels of organic pollutants with 99.7% accuracy, volatile solventswith 99.95% accuracy, and chlorinated compounds with 89.7%accuracy. If pollutants are not present the test does notsignal. Samples are prepared for the calibration of the testsand 60% of them are contaminated with organic pollutants, 27% withvolatile solvents, and 13% with traces of chlorinatedcompounds. A test is selected randomly.

a) What is the probability that the test will signal?
b) If the test signals, what is the probability that chlorinatedcompounds are present?

Explanation / Answer

The test signals a certain percentage ofthe time for each type so multiply each test success rate bypercentage of each test: (.997*.60)+(.9995*.27)+(.897*.13) = .984675= 98.47%
b) P[Chlorinate compounds | Test sginals] =P[Chlorinated compund and Test Signals]/P[TestSignals]

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