For Students · Birthday Paradox
Birthday Paradox for a sampling error
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a sampling error live below — adjust the inputs and watch it respond, right in your browser.
Birthday ParadoxLive
smaller than you'd think
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How many people until two share a birthday? Intuition says hundreds, but it takes just 23 for better-than-even odds, and 70 makes it near-certain. The trick is that the number of pairs grows quadratically — 23 people form 253 pairs, each a chance to match. It is why hash collisions and cryptographic birthday attacks happen far sooner than expected.
Data Inspector
Group size23
P(shared birthday)50.7%
Pairs253
Governing equation
Reading this result: Past the tipping point: 23 people form 253 pairs, and a match is now more likely than not (50.7%) — far fewer people than the 365 intuition expects.
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Frequently asked questions
- Is this good for students?
- Yes — this version of "Birthday Paradox for a sampling error" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.