Birthday Questions

 *    H  H
 *    H  H
 *    HHHH  aa ppp  ppp  y  y
 *    H  H a a p  p p  p y  y
 *    H  H aaa ppp  ppp   yyy
 *             p    p       y
 *             p    p    yyy
 *    BBBB          t  h       d
 *    B   B ii      t  h       d
 *    BBBB     rrr ttt hhh   ddd  aa y  y
 *    B   B ii r    t  h  h d  d a a y  y
 *    BBBB  ii r    tt h  h  ddd aaa  yyy
 *                                      y
 *                                   yyy

Today, in a not-so-veiled attempt to have everyone get more familiar with their classmates, I had everyone gather names and birthdays of everyone in each class and we looked for matching birthdays.

I prefaced this with these two questions about birthdays:

  1. What is the probability that at least two people in this class have the same birthday?
  2. How big a class would be required for that probability to reach 99%?

The answers are better than 50% for the first, with a class size of at least 23. For the second, surprisingly, it is only 57. (100% would require 366, of course.)

This is a classic problem in probability. Here’s a graph of the probabilities compared to the group size:


Extra credit for anyone who gives an explanation of the math behind this to the class.

We found 1, 3, and zero matches in periods 1, 2, and 3, respectively.


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