Chapter 6.6, Problem 14E

Exercises 11–15 refer to diagnostic tests. A false negative in a diagnostic test is a test result that is negative even though the patient has the condition. A false positive, on the other hand, is a test result that is positive although the patient does not have the condition.

Medical Screening A test for a condition has a high probability of false positives, 20%. Its rate of false negatives is 10%. The condition is estimated to exist in 65% of all patients sent for screening. If the test is positive, what is the chance the patient has the condition? Suppose that the condition is much more rare in the population—-say, Pr(condition) $=.30$. Given the same testing situation, what is Pr(condition pos)?