The Surprising Math Behind Shared Birthdays

Exploring the Birthday Paradox

Imagine walking into a room with 23 strangers. Someone mentions the Birthday Paradox, claiming there’s about a 50.7% chance that two people share a birthday. Skeptical, you wonder: “With 365 days in a year, how can the chance be so high?” Yet, mathematically, this intriguing claim holds true.

Let’s unravel the mystery step by step, explore why our intuition often deceives us, delve deeply into the fascinating mathematics behind it, and see practical applications in real-world scenarios.

Photo by Chris Benson on Unsplash

What Exactly Is the Birthday Paradox?

The Birthday Paradox explores the probability that, within a group of people, at least two will share the same birthday. Counterintuitively, this probability surpasses 50% with only 23 people and skyrockets to nearly 99.9% with just 70 people. Our confusion arises because we often approach probability linearly — “What’s the chance someone else shares my birthday?” — rather than combinationally — “What’s the chance any two people share a birthday?”

Why Our Intuition Fails

Humans typically think in terms of individual probabilities. The chance someone shares your birthday in a room of 23 people is relatively low, just 22/365 ~ 6.03%…