Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com/ The quick proof: https://www.youtube.com/watch?v=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 ------------------ 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. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u 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. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown