Monty Hall problem
Used as an illustration of how Bayesian reasoning (updating beliefs with new information) differs from naive probability, and how it can be a powerful tool for updating, but not for discovering new knowledge.
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Videos Mentioning Monty Hall problem

A.J. Jacobs — How to Be Less Furious and More Curious | The Tim Ferriss Show
Tim Ferriss
A famous probability puzzle where switching doors increases the odds of winning; discussed as a counter-intuitive puzzle.

Jeff Atwood: Stack Overflow and Coding Horror | Lex Fridman Podcast #7
Lex Fridman
Used as an example of how data and brute-force iteration can solve non-intuitive problems, demonstrating the power of empirical testing in programming.

The Beginning of Infinity, Part 1
Naval
Used as an illustration of how Bayesian reasoning (updating beliefs with new information) differs from naive probability, and how it can be a powerful tool for updating, but not for discovering new knowledge.