An Easier Counterintuitive Conditional Probability Problem (with and Without Bayes’ Theorem)

Given my recent posts about difficult counterintuitive probability problems (a topic from which I’ll now take a break for a while), I thought it’d be fun to briefly look at a problem that ceases to be counterintuitive once explained. This… Continue Reading

Share

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

Share

Counterintuitive Dice Probability: How many rolls expected to get a 6, given only even outcomes?

1. A Counterintuitive Probability Problem Mathematician Gil Kalai recently posted the following intuition-bending probability problem at his blog: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on… Continue Reading

Share

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

Share

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

Share

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

Share