Birthdays

Several times now I’ve been in a classroom situation where the professor has mentioned the well-known birthday paradox, and had the time and people to perform a demonstrative experiment, but didn’t seem as interested as I was. This morning I realized I could perform the experiment on my own without having to bother anybody else thanks to the magic of Facebook profiles. Since most people have their birthdays listed, I just opened up my list of friends alphabetically and starting listing birthdays to see how long it would take before one of them repeated:

1. Feb 2
2. Nov 26
3. Mar 29
4. Mar 14
5. Aug 27
6. Sep 30
7. Jul 6
8. Nov 24
9. Jun 3
10. May 8
11. Apr 23
12. Apr 20
13. Feb 2

Statistics says that there isn’t a better-than-average chance of a birthday collision until a group has at least 23 people in it. For only 13 people, as we have here, the probability of a collision is only

1 – (365!/352!)/365¹³ = 19.4%

Everybody try this at home!