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Category Archives: Probability
Test Your Intuition (10): How Does “Random Noise” Look
This is a bit unusual post in the “test your intuition” corner as the problem is not entirely formal. How does random noise in the digital world typically look? Suppose you have a memory of n bits, or a memory based on a larger … Continue reading
Answer to Test Your Intuition (9)
Two experimental results of 10/100 and 15/100 are not equivalent to one experiment with outcomes 3/200. (Here is a link to the original post.) One way to see it is to think about 100 experiments. The outcomes under the null … Continue reading
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
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
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 Chess, Gambling, Games of luck, Games of skill, Poker, Robert Aumann
37 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
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
13 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
