Template:Birthday problem

Try the birthday problem

Group size: 23 23

0%50%100%

In a group of 23 people, the probability that at least two share a birthday is 50.7%.

A shared birthday is more likely than not!

Deal random rooms

How often does a random room of that size really contain a match?

Deal a room of 23 people

Deal a room to see the result.

No room dealt yet - the boxes fill when you deal.

Jan 1 Jan 2 Jan 3 Jan 4 Jan 5 Jan 6 Jan 7 Jan 8 Jan 9 Jan 10 Jan 11 Jan 12 Jan 13 Jan 14 Jan 15 Jan 16 Jan 17 Jan 18 Jan 19 Jan 20 Jan 21 Jan 22 Jan 23 Jan 24 Jan 25 Jan 26 Jan 27 Jan 28 Jan 29 Jan 30 Jan 31 Feb 1 Feb 2 Feb 3 Feb 4 Feb 5 Feb 6 Feb 7 Feb 8 Feb 9

Each box is one person - a birthday drawn uniformly from 365 days, never re-rolled to force a result. Slide the group size to grow or shrink the room.

Long-run tally

Every deal of the same group size adds to this tally. Changing the slider starts a fresh tally on the next deal.

Rooms of 23	With a match	Match %	Expected
0	0	0.0	50.7%

▶ Auto-deal

Reset

50.7 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 23 1 50.7

The birthday problem at a glance (365 equally likely birthdays)

People in the group	Chance of a shared birthday
5	2.7%
10	11.7%
23	50.7%
30	70.6%
50	97.0%
70	99.9%

With just 23 people, a shared birthday is already more likely than not. An interactive version of this demonstration is available with JavaScript enabled.

Template documentation

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