So if we want to get pedantic, "random chord" is undefined here, which means that all the methods presented in the article as well as my sampling methods, and even the 0 and 1 case are all technically correct probabilities.
For example one of the most relatable alternative probabilities for me are, now thinking about it, actually the 0 or 1 cases: spinning a compass will generate a randomly oriented chord inside the face. What is the probability that the chord is of length > sqrt3? 1. Is this result informative or useful? no.
The result is that there are different generating functions with different biases which may or may not be useful. The three sources of randomness in the article correspond to physical stories that are possibly useful, and as such relatable. Otherwise they are no more legitimate than my absurdist examples.
For example one of the most relatable alternative probabilities for me are, now thinking about it, actually the 0 or 1 cases: spinning a compass will generate a randomly oriented chord inside the face. What is the probability that the chord is of length > sqrt3? 1. Is this result informative or useful? no.
The result is that there are different generating functions with different biases which may or may not be useful. The three sources of randomness in the article correspond to physical stories that are possibly useful, and as such relatable. Otherwise they are no more legitimate than my absurdist examples.