Version 1
: Received: 7 March 2023 / Approved: 8 March 2023 / Online: 8 March 2023 (10:10:49 CET)
How to cite:
Brazhnikov, P. Bertrand Paradox: Critical Consideration of Two of the Three Solutions in Terms of Geometry. Preprints.org2023, 2023030154. https://doi.org/10.20944/preprints202303.0154.v1
Brazhnikov, P. Bertrand Paradox: Critical Consideration of Two of the Three Solutions in Terms of Geometry. Preprints.org 2023, 2023030154. https://doi.org/10.20944/preprints202303.0154.v1
Cite as:
Brazhnikov, P. Bertrand Paradox: Critical Consideration of Two of the Three Solutions in Terms of Geometry. Preprints.org2023, 2023030154. https://doi.org/10.20944/preprints202303.0154.v1
Brazhnikov, P. Bertrand Paradox: Critical Consideration of Two of the Three Solutions in Terms of Geometry. Preprints.org 2023, 2023030154. https://doi.org/10.20944/preprints202303.0154.v1
Abstract
This article presents the results of the consideration of the Bertrand paradox in terms of geometric probability theory. Although the method and conclusions of this article are straightforward, no equivalent studies were found when reviewing the relevant literature. This could be conditioned by the fact that the hypotheses presented in this research have low intuitive obviousness and, in contrast, could be due to the historically established agreement regarding the issue. This article shows that out of three classical solutions to the problem described by Bertrand, two methods are inconsistent with the claimed relative objectivity. Although the remaining solution (1/4) seems to be the most correct, we cannot claim that we have exhaustively ruled out all aspects that could reduce its adequacy to solve the problem.
Keywords
Bertrand paradox; geometric probability; probability estimation method
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
