Geek Challenge: Baffling Birthdays

Geek Challenge

Ken Brey

10/04/2013

1 Comments

As school got back in session this fall, the first grade teachers at a large elementary school posted a list of student birthdays. The teachers noticed that of the 8 first grade classes at the school, 4 of the classes had students with duplicate birthdays. Each of the classes have just 23 students.

Is their observation a statistical anomaly, or it a highly probable?

What are the odds that a class of 23 students has one or more shared birthdays?

A: 5.8%
B: 50.0%
C: 50.7%
D: 75.0%

As always, the correct answer with the best engineering content will be our winner. Submit your responses to geekchallenge@dmcinfo.com.

Comments

# Joseph

Thursday, October 10, 2013 11:52 AM

Man, I hated prob and stats in school, but I remember this problem. The idea is to turn things on their head: consider the possibility that no 2 people out of a group will have matching birthdays. Use 365 days for the year (people born on leap days generally celebrate on March 1st or something like that) and assume even distribution throughout the year (actually a known falsehood). Anyhow, this Probability looks like this:
365!
___________________ = Q
(365-23)! * 365^23
But, we want the opposite of this probability, which is 1 - Q
Anyhow, run the numbers through Microsoft's calculator, and you get 50.72 %
So the answer is that this is quite probable. Given the true nature of births tending to cluster, the 'real' probability is even higher.
Please send me my check for 1 Million.

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