Larry Lesser
Engaging and Meaningful Connections
Larry Lesser

birthday

MoMath Math Encounters 1/15/2025 Larry Lesser talk: And One to Grow On: Lessons from the Birthday Problem

some BP RESOURCES 

real-world applications with BP structure

Post-Talk ACTIVITY 

Now that we know it takes just 23 randomly-selected people for a 50% chance of at least one birthday match, enjoy trying these explorations by yourself or with others:

  • For any number of people, see how close your intuition or simulation is by using the Wolfram Alpha BP calculator where you just enter a number of people (e.g., 23 or something else) and number of possible birthdays (e.g., 365) and it returns the probability of at least one match
  • Try the applet by James Jones (Richland Community College), enter 23 for “Number in Room,” and hit “Simulate” button lots of times. Do you get a match about half the time?  What if you change 23 to something else?  Or try this applet by UIUC folks.
  • See how repeated use of https://www.random.org/integers/ can simulate the probability: “Generate 23 random integers. Each integer should have a value between 1 and 365.”  Now, generate a larger sample (say, 50) of numbers (to be really confident there’s a match) and imagine the sample represents people arriving one at a time.  The average (expected value) position of the person that creates the first match is theoretically calculated as the 20th person.  Is that near the average position that created the first match in your repeated simulations?
  • Or use Excel spreadsheet software: in cell A1, enter =RANDBETWEEN(1,365), click on A1, click and hold the lower-right corner of A1 and drag it down to A23 and then let go. Then in an empty cell such as A25, enter =MODE(A1:A23) which returns #N/A if A1:A23 has no repeated number.  Here’s a related article.
  • If you have a Texas Instruments 83 or 84 calculator, try the steps below (want one for your smartphone or computer? download an emulator and rom, then click “Enable skin” from the calculator’s View dropdown menu): MATH –> randInt(1, 365, 23) STO –> 2nd –> ENTER;    STAT–> EDIT –> SortA –> ENTER –> 2nd L1 –> ENTER; STAT–> EDIT–> ENTER ; use the down arrow key to scroll down L1 to look for repeated numbers
  • Explore birthday probabilities with real-life data. For example, pick a major sports league (e.g., MLB, NFL, NHL, NBA, WNBA) and look up team rosters with player birthdays. Based on how many players are on a roster in that sport, you can use the WolframAlpha BP calculator to determine the probability of a match on a team, and therefore the expected proportion of team rosters in that sport that would have a match.  Try it!
  • real-life data (from CDC or SSA) on US births: https://github.com/fivethirtyeight/data/tree/master/births

my SONG, LETTERS, ARTICLES related to the BP 

  • L. Lesser (2014). Birthday dependence. Teaching Statistics, 36(2), 49.
  • L. Lesser (2013). And one to grow on: unwrapping the Birthday Problem. Mathematics Teacher, 106(8), 564, 565.
  • L. Lesser (2012). Birthday problem. Significance, 9(3), 46.
  • L. Lesser (2001). “Birthday Song“
  • L. Lesser (1999). Exploring the Birthday Problem with spreadsheets. Mathematics Teacher, 92(5), 407-411.
  • L. Lesser (1998). Richard von Mises. In D. R. Franceschetti (Ed.), Biographical Encyclopedia of Mathematicians, pp. 371-374. New York: Marshall Cavendish Corp.   NOTE: von Mises was first to publish the BP:  R. von Mises (1939). Über Aufteilungs–und Besetzungs-Wahrscheinlichkeiten.” Revue de la Faculté des Sciences de l’Université d’Istanbul, N. S. 4, 145-163.  Reprinted in P. Frank, S. Goldstein, M. Kac, W. Prager, G. Szegö, & G. Birkhoff (Eds.), Selected Papers of Richard von Mises, Vol. 2 (pp. 313-334), Providence, RI: American Mathematical Society, 1964.
  • Jane S. Grieg (1993, Sept. 6). Birthday coincidence noteworthy. Austin American-Stateman, 123(43), E1.
  • see this paper and Appendix C of another paper for overview of “counterintuitive examples”

ABSTRACT from flyer (or here) and registration page for archived talk: “The Birthday Problem is famous not only in math class – it’s also appeared in popular culture, such as in three straight episodes of The Tonight Show ! Join Larry Lesser, Professor in the Mathematical Sciences Department at The University of Texas at El Paso, as we test our intuition with this problem – and some interesting variations – while incorporating math history and the role of assumptions.  Even those who may have heard the main punchline will enjoy doing demonstrations and simulations, reflecting on how we perceive coincidence, and learning how the underlying reasoning applies to medical statisticians, criminologists, cybersecurity analysts, wildlife biologists, and more. Math Encounters is MoMath’s popular free public presentation series celebrating the spectacular world of mathematics.  This program is funded by Simons Foundation International and administered by the Simons Foundation’s Science, Society & Culture division.”  (note: update on Jim Simons)

NYC advance listings of event include: Patch, Club Free Time, FreeShows, FB