The birthday problem explained

Oct 5, 2012

How many people does it take for there to be a 50% chance that a pair in the group has the same birthday? Only 23 people. What about a 99% chance? Maybe even more shocking: 57 people. This is the birthday problem, which every undergrad who’s taken a stat course has seen. Steven Strogataz explains the logic and calculations.

Intuitively, how can 23 people be enough? It’s because of all the combinations they create, all the opportunities for luck to strike. With 23 people, there are 253 possible pairs of people (see the notes for why), and that turns out to be enough to push the odds of a match above 50 percent.

Incidentally, if you go up to 43 people — the number of individuals who have served as United States president so far — the odds of a match increase to 92 percent. And indeed two of the presidents do have the same birthday: James Polk and Warren Harding were both born on Nov. 2.

The Johnny Carson clip referenced in the article is worth watching. Carson tries to test the results with the audience, but goes about it the wrong way.

3 Comments

Favorites

Famous Movie Quotes as Charts

In celebration of their 100-year anniversary, the American Film Institute …

Real Chart Rules to Follow

There are rules—usually for specific chart types meant to be read in a specific way—that you shouldn’t break. When they are, everyone loses. This is that small handful.

Reviving the Statistical Atlas of the United States with New Data

Due to budget cuts, there is no plan for an updated atlas. So I recreated the original 1870 Atlas using today’s publicly available data.

Top Brewery Road Trip, Routed Algorithmically

There are a lot of great craft breweries in the United States, but there is only so much time. This is the computed best way to get to the top rated breweries and how to maximize the beer tasting experience. Every journey begins with a single sip.