Geodesic
An extended problem to Bertrand's paradox
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 23-34

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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.
Keywords: probability space, probability theory, problem modeling, random chords 
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Ardakani, Mostafa; Wulff, Shaun. An extended problem to Bertrand's paradox. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 23-34. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a1/