I taught math for many years, and this is the illustration I always used for Bayes’ Theorem:
Suppose 5% of the football team uses drugs, and they start using a drug test that is 95% accurate. If someone tests positive, what is the probability that they actually use drugs?
I won’t bore you with the actual formula, but imagine 10,000 people are tested. Of those, 5%, or 500 people, are using drugs. If 95% of them test positive, that’s 475 rightfully accused people. But, of the 9,500 non-users, 5% will also test positive (the test is only 95% accurate). So the actual probability that someone who tests positive on this 95% accurate drug test is actually using drugs is only 50%, not 95% as most people assume.
Good enough to ruin someone’s life over?
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