Three Strange Results in Probability: Cognitive States and the Principle of Indifference (Monty Hall, Flipping Coins, and Factory Boxes)

Probability is known for its power to embarrass our intuitions. In most cases, math and careful observation bear out counterintuitive results. After many such experiences, one’s intuition improves (sometimes perhaps crossing into a kind of overcorrection—see the Optional Endnote for… Continue Reading

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Nassim Taleb’s Fat Tony Example / And: Is it possible to flip 100 Heads in a row?

In his book The Black Swan, Nassim Nicholas Taleb, a fellow urban slow-walker, describes a scenario in which he poses the following question to two characters, the rational & educated Dr. John and the intuitive & streetwise Fat Tony: Assume that… Continue Reading

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Amnesiac’s Dilemma (Aka: Sleeping Beauty Problem)

There’s a probability problem that lacks an obvious solution, despite appearing simple at first glance. It’s usually called the Sleeping Beauty Problem, but I’m uncomfortable with that formulation, as it strikes me as needlessly sexist: it usually revolves around a young woman… Continue Reading

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