1.4.34. 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 the time. 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 the impurity?

1.4.34. 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 the time. 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 the impurity?

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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1.4.34. 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 the time. 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 the impurity?

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