probability on Dimitris Kokoretsis

The birthday problem — Part 3: Calculating in steps

Wed, 13 May 2026 00:00:00 +0000

“Good, fast, cheap. Choose two.” — expression of a universal sentiment: quality and precision are expensive and take time. This is the third and final part of the series on the birthday problem: What’s the probability that two students in a classroom share a common birthday? After mostly failing in part 1, we reached approximate answers in part 2. In this part, we will find the true pattern of the probability, translate it into code for precise calculations, and look back on the series through the prism of project management.

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.

The birthday problem — Part 1: When counting fails

Wed, 30 Nov 2022 00:00:00 +0000

After the “toy problem” of the previous post, I decided to take a chance at a more tangible, real-world question. Consider this one: What is the probability that two students in a classroom share the same birthday? Intuitively (and correctly), you might think it depends on the total number of students. But for a realistic classroom of around 20 students, the probability should be quite low - whatever “low” means. After all, how many times have you witnessed that?

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.