Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Birthday Paradox

Birthday Paradox for a fraud score

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a fraud score 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.

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Group size23

P(shared birthday)50.7%

Pairs253

Governing equation

P (n) = 1 - i = 0 \prod n - 1 \frac{365 - i}{365} = 1 - \frac{365 !}{( 365 - n )! 36 5 ^{n}} = 50.7% (n = 23)

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 k-12 students?: Yes — this version of "Birthday Paradox for a fraud score" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.