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Chance of sharing a birthday

Clinical bottom line

With 40 people in a room, there is a 90% chance that any two will share a birthday.

Even with 365 people in a room, there is only a chance of just below 1 in 2 that any two will share a particular birthday.


Data sources

Your brain.

What the sources tell us

  1. There are 365 days in a year. Only one day out of those 365 is a birthday.
  2. Therefore the chance of anyone having a birthday on a particular day is 1 in 365.

Give us the odds

The chance of:

The table gives the approximate odds. It rapidly becomes highly probable that two people will share a birthday when the number of people present is 40 or more.

The situation is different if you want to find the chance of someone sharing a particular birthday, when many more people are needed. The difference is that in the example of any birthday, the number of available days reduces. With a particular birthday, it is always 364/365. So instead of chances of 0.3%, 0.8%, and 1.6% with 2, 3 or four people, the chance becomes 0.3%, 0.5%, and 0.8% - with the gap rapidly growing.

So for the chance of two people sharing a particular birthday, with 25 people it is only 6%, with 100 people about 24%, with 200 people about 42%, and even with 365 people it is only about 60%

Table: Chance of two people sharing a birthday


Number of people
Probability
Chance %
Approximately 1 in
2
0.0027
0.3
370
3
0.0082
1
122
4
0.0164
2
61
5
0.0271
3
37
10
0.117
10
8.5
15
0.2529
25
4.0
20
0.4114
40
2.4
25
0.5687
60
1.8
30
0.7063
70
1.4
35
0.8144
80
1.2
40
0.9032
90
1.1
45
0.9483
95
1.1
50
0.9704
97
1.0
55
0.9863
99
1.0
60
0.9941
99.5
1.0

 

Comment

As always with risk and chance, the answer you get is about how you ask the question. Always listen carefully, and think.