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New Ways to Calculate the Probability in the Bertrand Problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • Javier Rodrigo & Mariló López & Sagrario Lantarón, 2023. "New Ways to Calculate the Probability in the Bertrand Problem," Mathematics, MDPI, vol. 12(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:3-:d:1302930
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    References listed on IDEAS

    as
    1. Richard A. Chechile, 2023. "Bertrand’s Paradox Resolution and Its Implications for the Bing–Fisher Problem," Mathematics, MDPI, vol. 11(15), pages 1-21, July.
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