The Birthday Paradox

The problem
23 people · 365 days

Twenty-three people are in a room. What's the probability that at least two of them share a birthday? Take a guess before scrolling.

Tempting (but wrong)
youvs365 days23 / 365 ≈ tiny?

Most people anchor on "365 days, 23 people" and reason: each person has a tiny chance of matching any specific date, so the room must have a tiny chance of producing a match. People often guess somewhere between 5% and 10%, or argue that you'd need closer to half of 365 — say 183 people — before the odds become reasonable.

This frames the problem incorrectly.