Related papers: Solving the Hard Problem of Bertrand's Paradox
We present a conclusive answer to Bertrand's paradox, a long standing open issue in the basic physical interpretation of probability. The paradox deals with the existence of mutually inconsistent results when looking for the probability…
Bertand's paradox is a fundamental problem in probability that casts doubt on the applicability of the indifference principle by showing that it may yield contradictory results, depending on the meaning assigned to "randomness". Jaynes…
We review the well known Bertrand paradoxes, and we first maintain that they do not point to any probabilistic inconsistency, but rather to the risks incurred with a careless use of the locution "at random". We claim then that these…
In this paper we report on an experimental test of Bertrand's question on the probability to find a random chord drawn inside a unit-radius circle with length greater than $\sqrt{3}$. In an experiment performed by tossing straws onto a…
This note is mainly to point out, if needed, that uncertainty about models and their parameters has little to do with a `paradox'. The proposed `solution' is to formulate practical questions instead of seeking refuge into abstract…
Simpson's paradox is an obstacle to establishing a probabilistic association between two events $a_1$ and $a_2$, given the third (lurking) random variable $B$. We focus on scenarios when the random variables $A$ (which combines $a_1$,…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
We investigate Bertrand's probabilistic paradox through the lens of discrete geometry and old-fashioned but reliable discrete probability. We approximate the plane unit circle with $1/n$ times $1/n$ boxes and count the pairs of boxes…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality,…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
Consider a free Schr\"odinger particle inside an interval with walls characterized by the Dirichlet boundary condition. Choose a parabola as the normalized state of the particle that satisfies this boundary condition. To calculate the…
Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…
Reichenbach's Common Cause Principle claims that if there is correlation between two events and none of them is directly causally influenced by the other, then there must exist a third event that can, as a common cause, account for the…
There has been an upsurge of interest in the consequences for quantum physics of the so-called Wigner's Friend Paradox. In its original formulation, the paradox has been turned inside out, and virtually every aspect of it has been looked…