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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Two-Child Problem (when one is a girl named Florida born on a Tuesday)

A classic probability riddle goes: A couple has two children, one of whom is a girl. What is the probability both children are girls? It’s usually credited to Martin Gardner who, in a 1959 issue of Scientific American, posed essentially this… 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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Why We Get the Monty Hall Problem Wrong(?)

Part I: The Monty Hall Problem The Monty Hall Problem (explained below) is one of those math results that strikes most people as counterintuitive. The problem is often illuminated by restating it with 100 doors instead of 3 doors. This makes many… Continue Reading

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