Estimating Pi

Sourced from Twitter on Pi Day (this also doubles up as a hint).

Take two random numbers $X$ and $Y$ between $0$ and $1$.

What is the probability that the integer nearest to $X/Y$ is even?

Solution

Folks, here’s one way to reason why this probability should be (5 - pi)/4.

Even if the math doesn’t appeal to you, please don’t miss the key lesson at the end! pic.twitter.com/IDEsQCuRVZ

— 10-K Diver (@10kdiver) March 15, 2022