# An extended problem to Bertrand's paradox

Mostafa K. Ardakani; Shaun S. Wulff

Discussiones Mathematicae Probability and Statistics (2014)

- Volume: 34, Issue: 1-2, page 23-34
- ISSN: 1509-9423

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topMostafa K. Ardakani, and Shaun S. Wulff. "An extended problem to Bertrand's paradox." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 23-34. <http://eudml.org/doc/271059>.

@article{MostafaK2014,

abstract = {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.},

author = {Mostafa K. Ardakani, Shaun S. Wulff},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {probability space; probability theory; problem modeling; random chords},

language = {eng},

number = {1-2},

pages = {23-34},

title = {An extended problem to Bertrand's paradox},

url = {http://eudml.org/doc/271059},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Mostafa K. Ardakani

AU - Shaun S. Wulff

TI - An extended problem to Bertrand's paradox

JO - Discussiones Mathematicae Probability and Statistics

PY - 2014

VL - 34

IS - 1-2

SP - 23

EP - 34

AB - 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.

LA - eng

KW - probability space; probability theory; problem modeling; random chords

UR - http://eudml.org/doc/271059

ER -

## References

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- [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. Zbl1052.60501
- [6] E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, New York, 2003). Zbl1045.62001
- [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). Zbl0605.60002

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