Perhaps the most important formula in probability.
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The quick proof:

Interactive made by Reddit user Thoggalluth:

The study with Steve:

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.


These animations are largely made using manim, a scrappy open-source python library:

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…