Monte-Carlo on Dimitris Kokoretsis

The birthday problem — Part 2: The statistical shortcut

Mon, 13 Jan 2025 00:00:00 +0000

In this post, we will answer a question that we previously failed at: What is the probability that two students in a classroom share the same birthday? This is described as a paradox because for a classroom of realistic size, the probability is surprisingly higher than intuitively expected. Previously, we could only solve this for very small classrooms of 2 or 3 students. The reason? Too much data. We will now get around this obstacle by the means of random sampling.

Football goals and coin flips: discovering the law of rare events

Mon, 08 May 2023 00:00:00 +0000

“To state a theorem and then to show examples of it is literally to teach backwards.” (E. Kim Nebeuts) Ever felt excited for discovering something that is already kinda known? Not necessarily for the discovery itself, but because you achieved it on your own and actually overcame an obstacle with it. This is how I feel about this story, and hopefully you will too. Starting from a small puzzle about football, we’re going to build the solution from scratch and see how -without knowing it- we just applied the law of rare events.

Drawing random biscuits: from probability to data

Sun, 28 Aug 2022 00:00:00 +0000

I stumbled upon a probability exercise when I had just built enough confidence with R scripting, and I was looking for “toy problems” to play with. It was a simple brain teaser, barely more complicated than the well-known coin toss. I could solve it with pen and paper, but I wanted to squeeze out of it as much as I could. My central thesis in this post is that, if we formulate our assumptions well, we can turn questions about probability into questions about data.