Daniel Litt @littmath

You are given an urn containing 100 balls; n of them are red, and 100-n are green, where n is chosen uniformly at random in [0, 100]. You take a random ball out of the urn—it’s red—and discard it. The next ball you pick (out of the 99 remaining) is:

More likely to be red 22.6%

More likely to be green 37.1%

Equally likely 20.9%

Don’t know/see results 19.5%

I thought it was interesting (but not surprising) that so many people got this wrong. Basically, Bayesian thinking is really foreign to people. It's essentially similar to the famous Monty Hall problem, where the first bit of information tells you something about the world. In any case, I thought it might be illuminating to give a complete demonstration, using both exact calculations AND simulation, of the "wrong" and "right" approach, which you can see at the Colab link above.