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A solution to the generalized birthday problem with application to allozyme screening for cell culture contamination

Published online by Cambridge University Press:  14 July 2016

M. H. Gail ,
G. H. Weiss ,
N. Mantel  and
S. J. O'Brien
M. H. Gail*
Affiliation:
National Cancer Institute, Bethesda, Maryland
G. H. Weiss*
Affiliation:
National Institutes of Health, Bethesda, Maryland
N. Mantel*
Affiliation:
George Washington University, Washington, D. C.
S. J. O'Brien*
Affiliation:
National Cancer Institute, Bethesda, Maryland
*
∗Postal address: National Cancer Institute, Landow Building, Room 5C-09, Bethesda MD 20014, U.S.A.
∗∗Postal address: Division of Computer Research and Technology, National Institutes of Health, Bethesda MD 20014, U.S.A.
∗∗∗Postal address: Biostatistics Center, George Washington University, Washington D.C. 20006, U.S.A. Research supported by Public Health Service Grant CA-15686 from the National Cancer Institute.
∗Postal address: National Cancer Institute, Landow Building, Room 5C-09, Bethesda MD 20014, U.S.A.
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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.

Keywords

GENERALIZED BIRTHDAY PROBLEMOCCUPANCYRECURSIVE SOLUTIONPROBABILITY APPROXIMATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 242 - 251
Copyright
Copyright © Applied Probability Trust 1979 

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