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)
Famous quotes containing the words classical and/or solution:
“Et in Arcadia ego.
[I too am in Arcadia.]”
—Anonymous, Anonymous.
Tomb inscription, appearing in classical paintings by Guercino and Poussin, among others. The words probably mean that even the most ideal earthly lives are mortal. Arcadia, a mountainous region in the central Peloponnese, Greece, was the rustic abode of Pan, depicted in literature and art as a land of innocence and ease, and was the title of Sir Philip Sidney’s pastoral romance (1590)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)