The birthday problem
Fill a room with people whose birthdays are random (365 equally likely days, ignoring 29 February). How often do two of them share a birthday? And how often does somebody share yours?
From the slides: Why should anyone care about chance? and Probability and what happens when you learn something.
Rooms simulated with this many people
0
Some two people share a birthday
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Somebody shares person 1's birthday
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Press Fill one room to see where the birthdays fall.
What to notice
- With 23 people a shared birthday is already more likely than not (0.507). With 60 it is almost certain (0.994).
- Somebody sharing your birthday is a completely different event: with 60 people it happens only about 15% of the time. A room of 60 has 1,770 pairs of people, but only 59 pairs involve you.
- Both formulas come from the complement: it is much easier to count the rooms with no match.
- Real birthdays are not quite uniform (more are in some months than others), which only makes matches more likely.