Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T07:19:30.311Z Has data issue: false hasContentIssue false
  • English
  • Français

On the generalised birthday problem

Published online by Cambridge University Press:  01 August 2016

R. J. McGregor  and
G. P. Shannon
R. J. McGregor
Affiliation:
School of Computing and Intelligent Systems, University of Ulster, Magee College, Londonderry, Northern Ireland BT48 7JL
G. P. Shannon
Affiliation:
School of Computing and Information Engineering, University of Ulster, Coleraine, Co. Londonderry BT52 1SA
Get access Rights & Permissions [Opens in a new window]

Extract

Probability theory abounds in counterintuitive results, perhaps the most celebrated being the answer to the birthday problem: what is the least value of n such that p (n, 2) > ½ where p (n, 2) denotes the probability that at least two out of n randomly chosen people have the same birthday? The question assumes birthdays are uniformly and independently distributed with leap years being ignored. The solution, n = 23, never fails to startle beginning students, and very often triggers an interest in the subject of probability. It is derived from the well-known observation that by the principle of complementation p (n, 2) is one minus the probability that no two have the same birthday, i.e.

Type
Articles
Information
The Mathematical Gazette , Volume 88 , Issue 512 , July 2004 , pp. 242 - 248
Copyright
Copyright © The Mathematical Association 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Feller, William, An introduction to probability theory and its applications, Wiley (1968).Google Scholar
2. Gehan, Edmund A., Note on the ‘Birthday Problem’, The American Statistician (1968) p. 28.Google Scholar
3. http://spring.infm.ulst.ac.uk/birthday Google Scholar