Classical Solution
The problem's classical solution thus hinges on the method by which a chord is chosen "at random". It turns out that if, and only if, the method of random selection is specified, the problem has a well-defined solution. There is no unique selection method, so there cannot be a unique solution. The three solutions presented by Bertrand correspond to different selection methods, and in the absence of further information there is no reason to prefer one over another.
This and other paradoxes of the classical interpretation of probability justified more stringent formulations, including frequency probability and subjectivist Bayesian probability.
Read more about this topic: Bertrand Paradox (probability)
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