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 (−) indicates that 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. In a recent article, a team of doctors discuss using a fever of 38°C or higher as a diagnostic indicator of postoperative atelectasis (collapse of the lung) as evidenced by x-ray observation. For fever ≥ 38°C as the diagnostic test, the results for postoperative patients are given below.   Condition Present Condition Absent Row Total Test Result + 65 31 96 Test Result − 80 76 156 Column Total 145 107 252 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.)  (e) P(condition present and +); this is the predictive value of the test. (f) P(condition present and −).

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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 (−) indicates that 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. In a recent article, a team of doctors discuss using a fever of 38°C or higher as a diagnostic indicator of postoperative atelectasis (collapse of the lung) as evidenced by x-ray observation. For fever ≥ 38°C as the diagnostic test, the results for postoperative patients are given below.

  Condition Present Condition Absent Row Total
Test Result + 65 31 96
Test Result − 80 76 156
Column Total 145 107 252

Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.) 

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


(f) P(condition present and −).

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