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Birthdays / 2009-10-18
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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!

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