The quick proof of Bayes' theorem

Watch on YouTube

Show annotations

Download is disabled.

209,954

8,105

55

Genre: Education

Family friendly? Yes

Wilson score: 0.9912

Rating: 4.973 / 5

Engagement: 3.89%

3Blue1Brown

Subscribe | 2.46M

Shared December 22, 2019

Including some added words on independence.
Main video: https://youtu.be/HZGCoVF3YvM
Brought to you by you: http://3b1b.co/bayes-thanks

------------------

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/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

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...
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown


L. A.

Can you maybe do a series about probability/statistics?

1 month ago | [YT] | 494

George Reynolds

You might think that this is just some mathematical issue, but the point made at 1:52 can have dramatic consequences. An English solicitor Sally Clark was convicted of killing her two baby sons on this same statistical error given as "evidence" by an eminent doctor (not statistician) and jailed. She served three years of a longer sentence before the Royal College of Statisticians intervened to point out the error of multiplying the probability of two children dying of the same cause, which was sudden infant death syndrome, and more likely to be genetic and in both children. Her career destroyed, she died from alcohol intoxication (suicide?) and the "eminent" doctor was struck off the medical registration list.

1 month ago (edited) | [YT] | 164

Jingchuan Shi

Two 3b1b in 10 minutes.
Is this early Christmas……

1 month ago | [YT] | 176

k0p1k4

ok so in short: simple multiplication of the probabilities is just a special case of Bayes’ theorem, when we have independence between events. therefore: P(A)=P(A|B).

1 month ago | [YT] | 22

Statici

Hopefully just a bit of constructive feedback: The bit at the start moving bars around representing where A and B are in terms of their probability is...not exactly intuitive. I'm still not entirely sure what the goal was with it; was an overlap intended to be shown? If so, well, it's just hard to see an overlap in that type of diagram.

Good video nonetheless though! Thanks for it and especially the main one.

1 month ago | [YT] | 162

Ashray Aggarwal

Calm down this is finally happening😍

1 month ago (edited) | [YT] | 8

Jascha

we just reiterated this in university two weeks ago ^^

1 month ago | [YT] | 3

Omar gaber

mathologer and 3Blue1Brown are my life.

1 month ago | [YT] | 7

Lightn0x

When I was first presented with this theorem, this is exactly the first thing I thought of. I thought "It's so obvious, how is this even helpful?". It was only later when I saw its many applications that I inderstood that a formula doesn't need to be complicated in order to be useful.

1 month ago | [YT] | 51

jsteele07189

This music is giving me Age Of Empires 3: The Age Of Kings vibes

1 month ago | [YT] | 0

dopamine addict

2 videos back to back. Christmas came early....

1 month ago | [YT] | 3

michael antoun

In the example given at 2:21, I noticed that the animation shows an increase in probability only horizontally, i.e. that your brother dying of heart disease means you are more likely to die of heart disease. Does it not also hold that if you die, of heart disease, your brother is then more likely to die of heart disease, implying a stretch not only horizontally but also vertically? If my thinking is incorrect, I'm very interested as to why.

1 month ago | [YT] | 20

DynestiGTI

Eagerly awaiting part 2. This is easily my newest favorite series of yours.

1 month ago | [YT] | 2

Fabio Vezzari

Soundtrack reminds me of the game spore, where you were able to make the anthem of your civilization

1 month ago | [YT] | 0

wffff2

Great, thanks for demystifying Bayes Theorem! Anytime I insist I know the basics of statistics, Bayes theorem is always there to raise an eyebrow.

1 month ago | [YT] | 0

Sayantan Maiti

today is National Mathematics Day of India for Ramanujan's Bday. and my favorite channel uploads. there's nothing greater than that.

1 month ago (edited) | [YT] | 40

Casimir P

Thank you. The tautophony on these Bayesian vids is amazing, just makes my ears close.

1 month ago | [YT] | 0

Santiago Bron

I remember when this channel had 500k subs.

1 month ago | [YT] | 0

Victor Hermes Torres Tomara

Now I like much more Bayes' theorem and I think it's implications of my way of thinking could be tremendous.

1 month ago | [YT] | 2

tbbmb

Dude... I finally understood Bayes' Theorem thanks to you. I wish my probability theory professor had given us these examples and methods.

1 month ago | [YT] | 0


33:59

Why was this visual proof missed for 400 years? (Fermat's two square theorem)

391K views

1:01:26

For the Love of Physics - Walter Lewin - May 16, 2011

2.3M views

10:44

P vs. NP and the Computational Complexity Zoo

2.3M views

10:45

5 of the World's Most Dangerous Chemicals

8.2M views

18:18

Hilbert's Curve: Is infinite math useful?

1.1M views

10:37

The Bayesian Trap

2.1M views

13:22

What if you could trade a paperclip for a house? | Kyle MacDonald | TEDxVienna

9.8M views

13:50

What's so special about Euler's number e? | Essence of calculus, chapter 5

1.3M views

16:30

Who cares about topology? (Inscribed rectangle problem)

1.4M views

13:44

What did NASA's New Horizons discover around Pluto?

5.1M views

18:39

This equation will change how you see the world

3.8M views

31:51

Visualizing quaternions (4d numbers) with stereographic projection

1.1M views

12:05

You know I’m all about that Bayes: Crash Course Statistics #24

139K views

20:25

What does the Laplace Transform really tell us? A visual explanation (plus applications)

350K views

32:11

Darts in Higher Dimensions (with 3blue1brown) - Numberphile

622K views

26:21

But how does bitcoin actually work?

3.1M views

17:05

The Essence of Calculus, Chapter 1

2.8M views

17:35

Bell's Theorem: The Quantum Venn Diagram Paradox

4.9M views