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

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 <span>_1/n_</span> chance and I did it <span>_n_</span> times, so the odds should be... <span>_63%_</span>. 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.