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:

Image: en.wikipedia.org/wiki/File:Birthday_Paradox.svg

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.

Comments are closed.