I once saw an interesting math challenge: Assume X and Y are randomly chosen numbers, with each being equally likely to be any number between 0 and 1. Take Y/X and round to the closest integer. What is the probability that this number will be even (or odd)?

It turns out this problem involves using the a ratio distribution. I felt that Wikipedia’s page on this subject was very poor, at the very least certainly unintuitive, so I hoped to come up with a more intuitive explanation.

(Note: This post does assume familiarity with probability distributions, using them to get cumulative distributions, averages, etc.)