The sensitivity of a test is the probability that a person, Ask an Expert

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Medical tests are used to indicate whether a person has a particular disease.

The sensitivity of a test is the probability that a person having the disease will test positive (indicating the person has the disease, i.e., it's the probability the test will pick up the fact that a person has the disease).

The specificity of a test is the probability that a person not having the disease will test negative.

A test for a certain disease has been in use for many years. Based on the "track record" of this test, its sensitivity is .934 and its specificity is .968. Finally, in the population, 1 in 500 people has the disease.

a) What is the probability that a person who tests positive actually has the disease?

b) What value would the specificity of the test have to have in order for the probability to exceed .5 that a person who tests positive actually has the disease?

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