Yet Another Paradox Paper: A Canonical-Measure Resolution of Bertrand’s Chord Problem

In geometric probability theory, whenever a geometric object, such as a point or line, is directed to be drawn at random but a sampling method is not specified, the standard interpretation is that we are to use the restriction and normalization of the canonical measure on the ambient space. This standard interpretation is what gives meaning to phrases like “a number is chosen at random between 0 and 100,” where the restriction and normalization of Lebesgue measure on the real line are universally understood, and allows us to provide a definitive answer to Bertrand's famous question: “One draws at random a chord in a circle. What is the probability that it is smaller than the side of the inscribed equilateral triangle?”