A Solution to the Generalized Birthday Problem with Application to Allozyme Screening for Cell Culture Contamination
Journal of Applied Probability
Generalized birthday problem, Occupancy, Recursive solution, Probability approximations
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.
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. https://nsuworks.nova.edu/cnso_bio_facarticles/185