Veritasium: The Bayesian Trap

Imagine during your routine checkup a doctor randomly suggests you to take a test, which would tell (with 99% accuracy) if you have a rather rare disease (only 0.1% people have it). Is it worth to be curious? What would you do if you test positive? Panic? Shock? The test is 99% accurate!

Now imagine that you have 1000 people. Only one of them (0.1%) will have this disease and there is a rather significant probability that he will test positive. Likely 10 people, out of 999 healthy people, will also test positive (1%). So in the end you have 11 positive results and only 1 sick person in the group. So actually there is only 9% chance that you actually have this disease.

This "paradox" is not a mathematical paradox, nor its a mathematical trick. It is actually Bayesian trap! More on it in the following video by Veritasium.