Medical Testing A test for a condition has a high probabilit

Medical Testing 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 6f)% 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)?

Solution

pr ( false positive ) = .20

pr ( positive) = .80

pr ( false negative ) = .10

pr ( all ) = .65

pr ( condition | pos ) = pr (all ) / pr ( pos )

pr ( condition | pos ) = .65 / .80 = .8125