A chemist wishes to detect an impurity in a certain compound that she is making.

Question

A chemist wishes to detect an impurity in a certain compound that she is making. There is a test that detects an impurity with probability 0.90; however, this test indicates that an impurity is there when it is not about 5% of the time. the chemist produces compounds with the impurity about 20% of time; that is, 80% do not have the impurity. A compound is selected at random from the chemist's output. The test indicates that an impurity is present. What is the conditional probability that the compound actually has an impurity?

Explanation / Answer

true positive; probability = 0.9 x 0.2 = 0.18 False positive, probability = 0.05 x 0.8 = 0.04. Therefore, the probablity you seek is 0.18/0.22 = 9/11

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