The birthday problem: chance that two people in a group share a birthday

Name: The birthday problem: chance that two people in a group share a birthday
Creator: Unlabeled
License: Original computation by Unlabeled; nothing copied from the source

With 23 people in a room the chance that two of them share a birthday is already 50.7%. With 57 people it is 99%.

What does this axis measure?

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y ↑: Chance of a shared birthday (%)
x →: Group size (people)

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The data: 40 points

Group size (people)	Chance of a shared birthday (%)
1	0
3	0.8
5	2.7
7	5.6
9	9.5
11	14.1
13	19.4
15	25.3
17	31.5
19	37.9
21	44.4
23	50.7
25	56.9
27	62.7
29	68.1
31	73
33	77.5
35	81.4
37	84.9
39	87.8
41	90.3
43	92.4
45	94.1
47	95.5
49	96.6
51	97.4
53	98.1
55	98.6
57	99
59	99.3
61	99.5
63	99.7
65	99.8
67	99.8
69	99.9
71	99.9
73	100
75	100
77	100
79	100

Source: Computed: the birthday problem with 365 equally likely birthdays
Licence: Original computation by Unlabeled; nothing copied from the source
Read: 2026-09-28
Drawn: 40 points as the puzzle showed them · line

Ran in puzzle #8 on October 4, 2026. Play it

The birthday problem: chance that two people in a group share a birthday

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