The Puzzle

There's a simple Monty Hall adjacent probability puzzle that goes like this:

Puzzle 1
I have two children, at least one of whom is a boy. What is the probability that both children are boys?

A more complex variation recently went viral on Twitter:

Puzzle 2
I have two children, (at least) one of whom is a boy born on a Tuesday — what is the probability that both children are boys?

Then Isaac King tweeted an even more complex variation:

Puzzle 3
I have two children, at least one of whom is a boy born on a day that I'll tell you in 5 minutes. What is the chance that both are boys, and what will the chance be after I tell you the day?

All three versions are fun and worth a try if you want to learn and practice Bayesian reasoning.

Personally, I found [...]

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Outline:

(00:05) The Puzzle

(01:46) The Solution

(02:19) Now the tricky part...

(03:09) Now the confusing part...

(06:24) More Bayesian analysis

The original text contained 3 images which were described by AI.

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First published:
January 2nd, 2025

Source:
https://www.lesswrong.com/posts/7i4qTDCxf5QBYWqvg/practicing-bayesian-epistemology-with-two-boys-probability

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Narrated by TYPE III AUDIO.

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“Practicing Bayesian Epistemology with ‘Two Boys’ Probability Puzzles” by Liron

LessWrong (30+ Karma)

“Practicing Bayesian Epistemology with ‘Two Boys’ Probability Puzzles” by Liron