Category Archives: Probability

Buffon’s Needle and the Perimeter of Planar Sets of Constant Width

Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David Eppstein.) (From Wolfram Mathworld) Buffon’s needle problem asks to find the probability that a needle of length will land on a line, given a floor … Continue reading

Posted in Convexity, Probability, Test your intuition | Tagged | 5 Comments

Test Your Intuition (7)

Consider the following game: you have a box that contains one white ball and one black ball. You choose a ball at random and then return it to the box. If you chose a white ball then a white ball is added to … Continue reading

Posted in Probability, Test your intuition | Tagged | 26 Comments

Chess can be a Game of Luck

Can chess be a game of luck? Let us consider the following two scenarios: A) We have a chess tournament where each of forty chess players pay 50 dollars entrance fee and the winner takes the prize which is 80% … Continue reading

Posted in Controversies and debates, Economics, Games, Law, Probability, Rationality | Tagged , , , , , | 38 Comments

Answer To Test Your Intuition (4)

Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading

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

Test Your Intuition (4)

Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading

Posted in Probability | 18 Comments

Some Philosophy of Science

The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentieth-century philosophers of science who later proposed alternative approaches. It will be convenient to start with … Continue reading

Posted in Philosophy, Probability | 14 Comments

A Problem on Planar Percolation

Conjecture (Gady Kozma):  Prove that the critical probability for planar percolation on a Cayley graph of the group is always an algebraic number. Gady  mentioned this conjecture in his talk here about percolation on infinite Cayley graphs.  (Update April 30: Today Gady mentioned … Continue reading

Posted in Open problems, Probability | Tagged , | 1 Comment

A Conference and a School on Oded Schramm’s Mathematics

There will be a conference this summer in Redmond and a school in December in Jerusalem devoted to Oded Schramm’s mathematics.   Oded Schramm Memorial Conference Probability and Geometry Redmond WA, August 30-31, 2009       To be held at Microsoft … Continue reading

Posted in Conferences, Probability | Tagged | 6 Comments

Noise Sensitivity Lecture and Tales

  A lecture about Noise sensitivity Several of my recent research projects are related to noise, and noise was also a topic of a recent somewhat philosophical post.   My oldest and perhaps most respectable noise-related project was the work with Itai Benjamini and Oded … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability | Tagged , , , , , , | 12 Comments

Test Your Intuition (1)

Question:  Suppose that we sequentially place balls into boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability balls in it. Suppose instead that … Continue reading

Posted in Computer Science and Optimization, Probability, Test your intuition | Tagged | 11 Comments