An extended problem to Bertrand's paradox

• Autorzy: Mostafa K. Ardakani , Shaun S. Wulff
• Języki publikacji: EN

Abstrakty

EN

Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination of the probability space.

Słowa kluczowe

EN

probability space; probability theory; problem modeling; random chords

Kategorie tematyczne

• 97K99: None of the above, but in this section
• 97G99: None of the above, but in this section
• 60D99: None of the above, but in this section
• 60A99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2014
• Tom: 34
• Numer: 1-2
• Strony: 23-34

Daty

wydano

2014

otrzymano

2014-03-14

Twórcy

autor

Mostafa K. Ardakani

• School of Engineering Technology, State University of New York, Farmingdale, NY, USA

autor

Shaun S. Wulff

• Department of Statistics, University of Wyoming Laramie, WY, USA

Bibliografia

• [1] L. Basano and P. Ottonello, The ambiguity of random choices: probability paradoxes in some physical processes, Amer. J. Phys. 64 (1996) 34-39. doi: 10.1119/1.18289.
• [2] J.L.F. Bertrand, Calcul des Probabilities (Gauthier-Villars, Paris, 1889).
• [3] S.S. Chiu and R.C. Larson, Bertrand's paradox revisited: more lessons about that ambiguous word, random, Journal of Industrial and Systems Engineering 3 (2009) 1-26.
• [4] M. Gardiner, Mathematical games: problems involving questions of probability and ambiguity, Scientific American 201 (1959) 174-182.
• [5] J. Holbrook and S.S. Kim, Bertrand's paradox revisited, Mathematical Intelligencer 22 (2000) 16-19.
• [6] E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, New York, 2003).
• [7] E.T. Jaynes, Well-posed problem, Foundations of Physics 3 (1973) 477-493.
• [8] L. Marinoff, A resolution of Bertrand's paradox, Philosophy of Science 61 (1994) 1-24. doi: 10.1086/289777.
• [9] G.J. Szekely, Paradoxes in Probability Theory and Mathematical Statistics (Kluwer Academic Publishers, New York, 1986).

Identyfikatory

DOI

10.7151/dmps1160