Perhaps the most important formula in probability.
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Special thanks to these supporters: http://3b1b.co/bayes-thanks
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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.

Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example

Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo

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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 expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
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https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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