New Ways to Calculate the Probability in the Bertrand Problem

Javier Rodrigo, Mariló López () and Sagrario Lantarón
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Javier Rodrigo: Departamento de Matemática Aplicada, Universidad Pontificia Comillas, 28015 Madrid, Spain
Mariló López: Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Sagrario Lantarón: Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Mathematics, 2023, vol. 12, issue 1, 1-10

Abstract: We give two new ways of calculating the probability of a chord of circumference randomly selected being larger than the side of an equilateral triangle inscribed in the circumference (this problem is known as the Bertrand paradox). The first one employs an immersion in R 4 , and the second one uses a direct probability measure over the set of chords.

Keywords: probability measures; Bertrand paradox; invariances (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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