Many diagnostic tests for detecting diseases do not test for the disease directly but for a chemical or biological product of the disease, hence are not perfectly reliable. The sensitivity of a test is the probability that the test will be positive when administered to a person who has the disease. The higher the sensitivity, the greater the detection rate and the lower the false negative rate. Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 85%. A person who actually has the disease is tested for it using this procedure by two independent laboratories. The probability that both test results will be positive is? The probability that at least one of the two test results will be positive

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Many diagnostic tests for detecting diseases do not test for the disease directly but for a chemical or biological product of the disease, hence are not perfectly reliable. The sensitivity of a test is the probability that the test will be positive when administered to a person who has the disease. The higher the sensitivity, the greater the detection rate and the lower the false negative rate.

Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 85%. A person who actually has the disease is tested for it using this procedure by two independent laboratories.

The probability that both test results will be positive is?

The probability that at least one of the two test results will be positive?

 

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