Bertrands Paradox Revisited:More Lessons about that Ambiguous Word, Random

The bertrand paradox question is: “consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals √3 . determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than √3 .” bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random.here we employ geometric and probability arguments to extend bertrand’s analysis in two ways: (1) for his three classic examples, we derive the probability distributions of the chord lengths; and (2) we also derive the distribution of chord lengths for five new plausible interpretations of randomness. this includes connecting (and extending) two random points within the circle to form a random chord, perhaps being a most natural interpretation of random.