Abstract

distributions obtained from transformation groups, using as our main example the famous paradox of Bertrand. Bertrand's problem (Bertrand, 1889) was stated originally in terms of drawing a straight line "at random" intersecting a circle. It will be helpful to think of this in a more concrete way; presumably, we do no violence to the problem (i.e., it is still just as "random") if we suppose that we are tossing straws onto the circle, without specifying how they are tossed. We therefore formulate the problem as follows. A long straw is tossed at random onto a circle; given that it falls so that it intersects the circle, what is the probability that the chord thus defined is longer than a side of the inscribed equilateral triangle? Since Bertrand proposed it in 1889 this problem has been cited to generations of students to demonstrate that Laplace's "principle of indifference" contains logical inconsistencies. For, there appear to be many ways of defining "equally possibl

Citations

224	The Classical Groups - Weyl - 1939
133	Prior probabilities - Jaynes - 1968
34	Introduction to Mathematical Probability - Uspensky - 1937
23	Probability, Statistics and Truth - Mises - 1939
15	Calcul des probabilités - Bertrand
4	Fifty Challenging Problems in Probability - Mosteller - 1987
4	Calcul des probabilitiés - Poincaré - 1912
3	Lady Luck: The theory of probability - Weaver - 1963
2	Éléments de la Théorie de Probabilités. Hermann 1909. 2nd edition 1910, 3rd edition 1924. New revised ed. published - Borel - 1965
1	The Theory of Probability, Chelsea Publ - Gnedenko - 1962
1	Riddles in mathematics - Northrup - 1944