Category Archives: Probability

Oz’ Balls Problem: The Solution

Posted on May 17, 2013 by

A commentator named Oz proposed the following question: You have a box with n red balls and n blue balls. You take out each time a ball at random but, if the ball was red, you put it back in the box and take out … Continue reading →

Posted in Probability, Test your intuition | Tagged , , , | 1 Comment

Taking balls away: Oz’ Version

Posted on April 27, 2013 by

This post is based on a comment by Oz to our question about balls with two colors: “There is an interesting (and more difficult) variation I once heard but can’t recall where: You have a box with n red balls … Continue reading →

Posted in Guest post, Probability, Test your intuition | Tagged , , | 14 Comments

Answer to test your intuition (18)

Posted on April 23, 2013 by

You have a box with n red balls and n blue balls. You take out balls one by one at random until left only with balls of the same color. How many balls will be left (as a function of n)? … Continue reading →

Posted in Probability, Test your intuition | Tagged , , , , | 3 Comments

Itai Ashlagi, Yashodhan Kanoria, and Jacob Leshno: What a Difference an Additional Man makes?

Posted on April 19, 2013 by

We are considering the stable marriage theorem. Suppose that there are n men and n women. If the preferences are random and men are proposing, what is the likely average women’s rank of their husbands, and what is the likely average … Continue reading →

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Test Your Intuition (19): The Advantage of the Proposers in the Stable Matching Algorithm

Posted on April 9, 2013 by

Stable mariage The Gale-Shapley stable matching theorem and the algorithm. GALE-SHAPLEY THEOREM Consider a society of n men and n women and suppose that every man [and every woman] have a preference (linear) relation on the women [men] he [she] knows. Then … Continue reading →

Posted in Combinatorics, Games, Probability, Test your intuition | Tagged , , , , , , | 7 Comments

Test Your Intuition (18): How many balls will be left when only one color remains?

Posted on April 3, 2013 by

(Thanks to Itai Benjamini and Ronen Eldan.) Test (quickly) your intuition:  You have a box with n red balls and n blue balls. You take out balls one by one at random until left only with balls of the same … Continue reading →

Posted in Probability, Test your intuition | 24 Comments

What does “beyond a reasonable doubt” practically mean?

Posted on June 13, 2012 by

(Motivated by two questions from Gowers’s How should mathematics be taught to non mathematicians.)

Posted in Law, Probability, Test your intuition | 18 Comments

Noise Sensitivity and Percolation. Lecture Notes by Christophe Garban and Jeff Steif

Posted on November 6, 2011 by

Lectures on noise sensitivity and percolation is a new beautiful monograph by Christophe Garban and Jeff Steif. (Some related posts on this blog: 1, 2, 3, 4, 5)

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Is Backgammon in P?

Posted on January 14, 2011 by

  The Complexity of Zero-Sum Stochastic Games with Perfect Information Is there a polynomial time algorithm for chess?  Well, if we consider the complexity of chess in terms of the board size then it is fair to think that the answer is … Continue reading →

Posted in Computer Science and Optimization, Games, Open problems, Probability | 9 Comments

Emmanuel Abbe: Erdal Arıkan’s Polar Codes

Posted on November 25, 2010 by

Click here for the most recent polymath3 research thread. A new thread is comming soon.   Emmanuel Abbe and Erdal Arıkan This post is authored by Emmanuel Abbe A new class of codes, called polar codes, recently made a breakthrough … Continue reading →

Posted in Information theory, Probability | Tagged , | 17 Comments