IJPAM: Volume 81, No. 6 (2012)


Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN

Abstract. This article presents 2 unexpected probabilities. If there are at least 23 people in a class, then the probability that there is a shared birthday exceeds one half. This is explained by the idea of complementary events. What are the chances of there being a student who ends up in the same seat when everyone in the class is reseated? This probability is around $\displaystyle{\frac{2}{3}}$ irrespective of the number of students, and was solved by Montmort (1708).

Received: August 18, 2012

AMS Subject Classification: 60A02, 00A09, 97A20

Key Words and Phrases: likelihood of shared birthdays, complementary events, probability of ending up in the same seat, Montmort's theory, Venn diagram

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 6