Question: Diagnostic tests of medical conditions have several results. The test result can be positive or negative, whether or not a patient has the condition. A positive (+) indicates the patient has the condition. A negative test (-) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown:

Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities.

(a) P(+, given condition present); this is known as the sensitivity of a test.

(b) P(-, given condition present); this is known as the false-negative rate.

(c) P(-, given condition absent); this is known as the specificity of a test.

(d) P(+, given condition absent); this is known as the false-negative rate.

(e) P(condition present and +); this is the predictive value of the test.

(f) P( condition present and -).