A Solution to the Generalized Birthday Problem with Application to Allozyme Screening for Cell Culture Contamination

Authors

• M. H. Gail, National Cancer Institute at Bethesda
• G. H. Weiss, National Institutes of Health at Bethesda
• N. Mantel, George Washington University
• Stephen J. O'Brien, National Cancer Institute at BethesdaFollow

ORCID

0000-0001-7353-8301

ResearcherID

N-1726-2015

Document Type

Article

Publication Title

Journal of Applied Probability

ISSN

0021-9002

Publication Date

6-1979

Keywords

Generalized birthday problem, Occupancy, Recursive solution, Probability approximations

Abstract

This paper gives the probability that no common allozyme signature is found among n randomly selected cell culture lines when the s mutually exclusive and exhaustive signatures have arbitrary known probabilities. This result is useful in detecting cell culture contamination by a single cell line. This problem is a generalization of the classic problem of finding the probability of no common birthday among n individuals when it is assumed that each individual has a chance 1/s = 1/365 of a birthday on a given day. Both an exact recursive solution and an approximate solution are given for the general problem.

DOI

10.2307/3212893

Volume

16

Issue

2

First Page

242

Last Page

251

Comments

©1979 Applied Probability Trust

NSUWorks Citation

Gail, M. H.; G. H. Weiss; N. Mantel; and Stephen J. O'Brien. 1979. "A Solution to the Generalized Birthday Problem with Application to Allozyme Screening for Cell Culture Contamination." Journal of Applied Probability 16, (2): 242-251. doi:10.2307/3212893.