The question
Birthday paradox: what’s the chance at least two of them share a birthday?
23 people are in a room. Birthdays are random: each of 365 days equally likely, independent of each other, ignoring leap day.
Model used: 365 equally likely birthdays, independent, no leap day, no twins.
Your bet — tap one
Bet first: the 100,000-trial run unlocks after you pick.
Reality check
0trials ·
The aha
You’re not matching your birthday — you’re matching any pair.
23 people make 23 × 22 ÷ 2 = 253 different pairs, and every pair is a chance for a match.
Each pair only matches 1 time in 365, but 253 small chances add up fast: by 23 people it’s just over a coin flip.
Matching your own specific birthday is a different question — that takes about 253 other people for a 50% chance.
Try it yourself: mathahadaily.kairoxbuild.com/lab