Resources
Birthday Problem and Class Phenotypic Probabilities
Author(s): John R Jungck1, Jennifer Spangenberg2, Annelise L. Myers2
1. Interdisciplinary Science Learning Center at the University of Delaware 2. Beloit College
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Birthday_Problem_edited.xls(XLS | 409 KB)- License terms
Overview
This workbook as two related applications, the Birthday Problem and Class Phenotypic Probabilities. The Birthday Problem calculates the probability that two people in a given number will have the same birthday. The user will enter their class number into the worksheet and the program will output a probability, graphically. Class Phenotypic Probabilities determines the allelic frequency of a population for 6 characteristics (blood type, RH positive/negative, sex, mid-digital hair positive/negative, earlobes attached/unattached and PTC taste receptor). The user can enter their phenotype for each characteristic and the program will calculate the probability of that particular combination and the probability of other people having the same combination.
Popular Text Citations
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. New York: Wiley, pp. 31-32.
Hunter, J. A. H. and Madachy, J. S. (1975) Mathematical Diversions. New York: Dover, pp. 102-103.
Ball, W. W. R. and Coxeter, H. S. M. (1987) Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 45-46.
Research Articles
Riesel, H. (1994) Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp.179-180.
Diaconis, P. and Mosteller, F. (1989) "Methods for Studying Coincidences." J. Amer. Statist. Assoc. 84: 853-861 .
Clevenson, M. L. and Watkins, W. (1991) "Majorization and the Birthday Inequality." Mathematics Magazine 64: 183-188.
Sayrafiezadeh, M. (1994) "The Birthday Problem Revisited." Mathematics Magazine 67: 220-223.
Abramson, M. and Moser, W. O. J. (1970) "More Birthday Surprises." American Mathematical Monthly 77: 856-858.
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Levin, B. (1981) "A Representation for Multinomial Cumulative Distribution Functions." Annals of Statistics 9, 1123-1126.
Stewart, I. (June 1998) "What a Coincidence!" Scientific American 278:95-96.
Hocking, R. L. and Schwertman, N. C. (1986) "An Extension of the Birthday Problem to Exactly k Matches." College Mathematics Journal 17: 315-321.
Heuer, G. A. (1959) "Estimation in a Certain Probability Problem." American Mathematical Monthly 66: 704-706.
McKinney, E. H. (1996) "Generalized Birthday Problem." American Mathematical Monthly 73: 385-387.
Klamkin, M. S. and Newman, D. J. (1967) "Extensions of the Birthday Surprise." Journal of Combinatorics Th. 3: 279-282.
Bloom, D. M. (1973) "A Birthday Problem." American Mathematical Monthly 80: 1141-1142.
Education Research & Pedagogical Materials
Lesser, L.M. (1999). Exploring the birthday problem with spreadsheets, The Mathematics Teacher (92), No. 5 pp. 407-411.
Stultz, Lowell. 2000. Probabilities and Statistics on the Spreadsheet. In 'How to Excel in Finite Math'. Pearson Custom Publishing, Boston, Pages 104-113.
Tutorial & Background Materials
Eric W. Weisstein. "Birthday Problem." From MathWorld--A Wolfram Web Resource.
Becky Schmoyer. The Birthday Problem
S. Finch. "Puzzle #28 [June 1997]: Coincident Birthdays."
Ivars Peterson. "MathTrek: Birthday Surprises." Nov. 21, 1998.
The Birthday Problem, University of Virginia (broken link - http://curry.edschool.virginia.edu/go/teacherlink/content/math/interactive/probability/lessonplans/birthday/home.html)
L. Tesler. "Not a Coincidence!"
Citation
Researchers should cite this work as follows:
- Jungck, J. R., Spangenberg, J., Myers, A. L. (2018). Birthday Problem and Class Phenotypic Probabilities. ESTEEM, QUBES Educational Resources. doi:10.25334/Q4CT69
Fundamental Mathematical Concepts
Developed By
Primary Reference
Mises, R. von. "Über Aufteilungs--und Besetzungs-Wahrscheinlichkeiten." Revue de la Faculté des Sciences de l'Université d'Istanbul, N. S. 4, 145-163, 1939. Reprinted in Selected Papers of Richard von Mises, Vol. 2 (Ed. P. Frank, S. Goldstein, M. Kac, W. Prager, G. Szegö, and G. Birkhoff). Providence, RI: Amer. Math. Soc., pp. 313-334, 1964.