A classic example would be that if you have a test (say for cancer) with a false positive rate of “””only””” 5%, and your disease has an incidence of say 1 in 1000.

Let’s say that you get a positive diagnosis for the disease, and you ask someone the question:

What is the probability you actually have the disease?

Most people will say 95% or 99%, but your actual probability of having the disease in this example is <2%