A chemist wishes to detect an impurity in a certain

Chapter 1, Problem 7E

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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 the 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?

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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 the 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?

ANSWER:

Step 1 of 3

We have,

Probability that the compound has impurities = P(A)

Probability that the compound does not has impurities = P(B)

Probability that the test detects impurity = P(I)

We need to find what is the conditional probability that the compound actually has an impurity?

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