The answer involves π because why wouldn't it? 🙃

If you take two random numbers between 0 and 1 and divide them, what's the probability that rounding the result will give you an even number? Spoiler: it involves everyone's favorite circle constant.


=Chapters=
0:00 - Intro
2:23 - Visualizing the probability
5:00 - Evaluating the sum
6:16 - Changing the problem slightly
8:43 - Evaluating another sum (the long way)
14:04 - A word about generating functions


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This video was generously supported in part by these patrons on Patreon:
Marshall Harrison, Michael OConnor, Mfriend, Carlos Herrado

Thanks for your support!


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CREDITS

The music tracks used in this video are (in order of first appearance): Icelandic Arpeggios, Checkmate, Rubix Cube, Orient

The track "Rubix Cube" comes courtesy of Audionautix.com


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The animations in this video were mostly made with a homemade Python library called "Morpho". It's mostly a personal project, but if you want to play with it, you can find it here:
github.com/morpho-matters/morpholib