Many diagnostic tests for detecting diseases do not test for the disease directl

Question

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 92%. A person who actually has the disease is tested for it using this procedure by two independent laboratories.

What is the probability that both test results will be positive?

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

Explanation / Answer

1)

P(both tests results would be positive) = P(1st and well as 2nd test result would be positive) = (0.92)(0.92) = 0.8464

2)

P(at least one of the 2 test results will be positive) = 1 - P(none of the 2 test resuslts will be positive)

= 1 - (1-0.92)(1-0.92) = 1 - 0.0064 = 0.9936

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