Suppose a person is chosen at random and is given a test for a disease. For example, imagine that this is a routine screening for a disease; the person may not have any symptoms. Suppose we know how effective the test is when it is given to a person who does have the disease (the probability the test is positive) and when given to a person who does not have the disease (the probability the test is negative). Furthemore, suppose we also know the percentage of the population that has the disease.
If a person tests postive, what is the probability that the person is ill?
The answer is to look at what percentage of positive tests are true positives.
Dave Richeson, Created with GeoGebra