If you take a group of people born in a non leap year you would need 366 people for a 100% chance that someone shares a birthday but only 23 people for a 50% chance that somebody shares a birthday?
In: Mathematics
Person A and B have a 1/365 chance of sharing a birthday amongst themselves. There’s one possible match.
Add person C to the group, and then A can now match with B as before, but they can also match with C, and B can now also match with C. That’s 3 possible matches
Add D, and then A can match with B, C or D; B can also match with C or D, and C can also match with D. That’s 6 possible matches.
In fact, the number of possible matches increases like this:
(Number of people) x (Number of people -1) / 2.
For 23 people, 23 * 22 = 253 pairs of people who could possibly share a birthday.
With this number being more than half the days in the year, it wouldn’t be more likely to find a pairing that shares a birthday in the group than no pairing shares a birthday.
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