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The Birthday Problem
“With 23 people, the simple model already gives a greater than 50% chance that some pair shares a birthday.”
01 / SUMMARY
In short
The surprise comes from counting pairs, not people. Twenty-three individuals create 253 possible pairs; every newcomer can match everyone already present.
03 / SCENE
In the wild
The question is not whether someone shares your birthday, but whether any pair in the group matches.
04 / LIMIT
The limit
The 50% figure assumes 365 equally likely, independent dates; real birthdays do not fit that model exactly.
FINAL NOTE
What remains
When looking for any collision, count every pair capable of producing one.