In this exercise, we consider a rare disease affecting 1% of the population and an accurate test for this disease – 99% accuracy. Despite this accuracy, we see in this exercise that you’re very unlikely to have the disease even if the test returns positive. How do we intuitively make sense of this?
The following image is a helpful aid for thinking about this problem.
As we can see here, although in a group of 1000 people there will be 95 true positives, that is, 95 people who both have the disease and receive a positive test, there are far more, 495 to be exact, false positives, that is, 495 people who don’t have the disease and receive a positive test. This is because 1% inaccuracy from a large group of people, the 99% of people who don’t have the disease, is still a large number and so outweighs the large percentage accuracy from a comparatively very small group.