Suppose a rare and fatal disease randomly afflicts 1 out of every 100,000 people in the population. Also suppose you are told, after being screened for the disease with a lab test that’s accurate 99.9% of the time, that you have the disease. Are you doomed?
Probably not, because there’s less than a 1% chance you actually have the disease!!!
This surprisingly low probability is given by Bayes’ theorem which can be proven in any of 4 ways: (1) with a simple 2×2 table containing frequency counts, (2) with a Venn diagram, (3) with a tree diagram, or (4) with a formula. Worth watching are 4 short videos that show these alternative ways to determine the conditional probability of having a disease “given that” the screening test is positive. Here are the links to these clear and informative videos: