(Demo by Chris Piech)


Problem

In this problem we are going to calculate the probability that a patient has an illness given a positive test-result for the illness. A positive test result means the test thinks the patient has the illness.

Things that we know: Naturally 8% of the population has the illness. The test returns a positive result 95% of the time for patients who have the illness. The test resturns a positive result 7% of the time for people who do not have the illness.


Answer

The probability that the patient has the illness given a positive test result is: