Category Archives: Probability


Pick randomly three points on the unit sphere. The geodesic triangle with these points as vertices divides the sphere into two parts. What is the probability that the north pole is contained in the smaller of these parts? For instance … Continue reading

Posted in Geometry, Mathematics, Probability, Wednesday Problem | Leave a comment

Prisoner’s problem 2

Please comment your solutions, questions and remarks.. Consider a prison with several millions prisoners. The head of the prison arranges the following challenge to the prisoners. One prisoner at a time will be called to a room with a lamp. … Continue reading

Posted in Mathematics, Probability, Recreation, Wednesday Problem | Tagged | 2 Comments

Andre’s Reflection Method

I promised to post something about random walks. I learned the content of this post while listening to Vilppu Tarvainen’s bachelor’s degree talk and I consider it is quite cute. Let us consider a one dimensional random walk: formally it … Continue reading

Posted in Combinatorics, Mathematics, Probability, Recreation | 1 Comment

Continuum Hypothesis III

Suppose you pick randomly a real number. What is the probability that it equals to 1? The probability is zero. Suppose [tex]X\subset [0,1][/tex] is a countable subset of the unit interval. What is the probability that a randomly picked real … Continue reading

Posted in Foundations, Mathematics, Philosophy, Probability, Set Theory | Tagged | 2 Comments

Where Do Random Walks Lead

Rami Luisto asked the following question: Pick randomly n unit vectors from the plane, [tex]x_1,\dots,x_n\in \mathbb{R}^2[/tex]. What is the probability that the sum of these vectors has magnitude less than or equal to one, [tex]|x_1+\cdots+x_n|\leqslant 1[/tex]? (magnitude = norm = … Continue reading

Posted in Calculus, Mathematics, Probability | 3 Comments

The Monkey and the Balls

I heard this story here at Mittag-Leffler institute from someone who heard it from someone else, who probably also heard it from someone else. (And so on.) What is the probability that I heard it from someone else? Just kidding. … Continue reading

Posted in Mathematics, Philosophy, Probability | 2 Comments