I know it sounds like a Yogi Berra quote but it is actually true.
https://www.concordmonitor.com/medical-tests-positive-statistics-27349847
https://www.concordmonitor.com/medical-tests-positive-statistics-27349847
Imagine a town of 10,000 people in which 1% of the population has a deadly disease. You want to find out who those people are using a test that’s 99% accurate, so you give the test to everybody.
There are 100 people in town who have the disease – that’s 1% of the total population – and the test finds 99 of them, missing just a single sick person. Well done!
But remember that 9,900 of the people who were tested do not have the disease. The test is 99% accurate so it knows that 9,801 of them are healthy. What a relief!
But since the test is sometimes wrong, it incorrectly says that 1% of the healthy people are infected. That’s 99 people, all of whose lives are turned upside down when they’re told (incorrectly) that they have a deadly disease.
Look at those results again. Testing the whole population for a rare disease produced 198 positive results, but one-half of them were wrong: 99 of the people were sick but 99 were actually healthy.
A 99% accurate result was wrong half the time. Truly that’s a Paradox from Prediction of Positive results. Triple P in action!