I present two exact approaches for efficiently computing the probability that an exponential random variable ranks kth among N independent exponentials with different rate parameters.

Inspired by a simple probability puzzle, I set out to determine the probability that a Poisson random variable is divisible by a given integer, before extending this result to calculate the distribution of the Poisson random variable modulo a divisor.

The Countdown numbers game is notoriously fiendish. That said, with the right computational tricks, it can be solved using only basic coding abilities.