“‘It’s a 10% chance which I did 10 times, so it should be 100%’” by egor.timatkov

LessWrong (Curated & Popular)

Audio note: this article contains 33 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.
Many of you readers may instinctively know that this is wrong. If you flip a coin (50% chance) twice, you are not guaranteed to get heads. The odds of getting a heads are 75%. However you may be surprised to learn that there is some truth to this statement; modifying the statement just slightly will yield not just a true statement, but a useful one.
It's a spoiler, though. If you want to figure this out as you read this article yourself, you should skip this and then come back. Ok, ready? Here it is:
It's a _1/n_ chance and I did it _n_ times, so the odds should be... _63%_. Almost always.

The math:
Suppose you're [...]
---
Outline:
(01:04) The math:
(02:12) Hold on a sec, that formula looks familiar...
(02:58) So, if something is a _1/n_ chance, and I did it _n_ times, the odds should be... _63\\%_.
(03:12) What Im NOT saying:
---
First published:
November 18th, 2024
Source:
https://www.lesswrong.com/posts/pNkjHuQGDetRZypmA/it-s-a-10-chance-which-i-did-10-times-so-it-should-be-100
---
Narrated by TYPE III AUDIO.