The Monty Hall Problem & Conditional Probability
Steve Selvin / Marilyn vos Savant · 1975
"Switching doors in Monty Hall doubles your chance of winning from 1/3 to 2/3 — because the host's action of opening a losing door is not random, it leaks information about where the prize isn't."
You pick one of three doors. The host, who knows what's behind each, opens a different losing door and offers you the switch. Intuition screams 50/50. The math says switch and you win two-thirds of the time.
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P vs NP & Computational Complexity
"Cook and Levin formalized the most important open question in computer science: if a solution can be verified quickly (NP), can it also be found quickly (P)? Most experts believe no — and that gap explains why many optimization, routing, and scheduling problems have no efficient perfect solution."