Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (ˆ’) indicates that the patient does not have the condition. Remember, a positive test does not prove that 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(+ | condition present); this is known as the sensitivity of a test.
(b) P(ˆ’ | condition present); this is known as the false-negative rate.
(c) P(ˆ’ | condition absent); this is known as the specificity of a test.
(d) P(+ | condition absent); this is known as the false-positive rate.
(e) P(condition present and + ); this is the predictive value of the test.
(f) P(condition present and ˆ’ ).

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in Absent Row Total Condition Condition Test Result Test Result Column Total Present 110 20 20 50 70 130 70 200