Perhaps the most important formula in probability.
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The quick proof: https://youtu.be/U_85TaXbeIo

Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/

The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf

You can read more about Kahneman and Tversky’s work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.

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These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it’s not the most well-documented tool, and it has many other quirks you might…

Source: https://www.youtube.com/watch?v=HZGCoVF3YvM