Related papers: Bertrand's paradox: a physical solution
Charles L. Dodgson, also known as Lewis Carroll, in his book "Pillow problems" from 1893 asked for the likelihood of a random triangle to be obtuse. Clearly, the answer to Dodgson's question depends strongly on the assumed random…
The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…
The problem of creating a three-sided dice with the probability of it landing on each of its sides being equal to 1/3 has been around for many years. Various approaches have been attempted, but as different authors achieved at different…
We present a variation of the broken stick problem in which $n$ stick lengths are sampled uniformly at random. We prove that the probability that no three sticks can form a triangle is the reciprocal of the product of the first $n$…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
The Delayed-Choice Quantum Eraser experiment is commonly interpreted as implying that in quantum mechanics a choice made at one time can influence an earlier event. We here suggest an extension of the experiment that results in a paradox…
The Erd\H{o}s-Straus conjecture is a renowned problem which describes that for every natural number $n~(\ge 2)$, $\frac{4}{n}$ can be represented as the sum of three unit fractions. The main purpose of this study is to show that the…
In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed…
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions…
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 $a_1$,…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…
It seems reasonable that a toroid can be thought of approximately as a solenoid bent into a circle. The correspondence of the inductances of these two objects gives an approximation for the natural logarithm in terms of the average of two…
The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum…
Parrondo paradox describes the counterintuitive phenomenon in which alternating two individually losing games yields a winning outcome. Extending this effect to the quantum regime has typically required high dimensional coin spaces,…
The 120-year old so-called Painleve paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal…
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum…
The title of the article is identical to the title of Chapter 21 in Gardner (2001): because we are going to analyze the probability calculations and the ambiguity of the problem statements. We will analyze 3 out of 4 problems from Gardner…