Diagnostic tests of medical conditions have several results. The rest result can

Question

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) 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 121 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. Condition Present Condition Absent Row Total Test Result + 103 18 121 Test Result – 18 51 69 Column Total 121 69 190 Assume that the sample is representative of the entire population. For a person selected at random, find P(Condition present|getting test result +). Round your answer to the nearest hundredth. a. 0.15 b. 0.54 c. 0.74 d. 0.85 e. none of these choices

Explanation / Answer

P( Condition present/ Test+) = P( Test+/ COndition present) * P(Condition present) /[P( Test+/ COndition present) * P(Condition present) +P( Test+/ COndition absent) * P(Condition absent)] = 103/121*121/190 / [103/121*121/190 + 18/69*69/190]= 103/121 = 0.85

Hence, D is the correct answer

103/121*121/190 / [103/121*121/190 + 18/69*69/190]

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