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Following the Daubert ruling in 1993, forensic evidence based on fingerprints was first challenged in the 1999 case of the U.S. versus Byron C. Mitchell and, subsequently, in 20 other cases involving fingerprint evidence. The main concern with the admissibility of fingerprint evidence is the problem of individualization, namely, that the fundamental premise for asserting the uniqueness of fingerprints has not been objectively tested and matching error rates are unknown. In order to assess the error rates, we require quantifying the variability of fingerprint features, namely, minutiae in the target population. A family of finite mixture models has been developed in this paper to represent the distribution of minutiae in fingerprint images, including minutiae clustering tendencies and dependencies in different regions of the fingerprint image domain. A mathematical model that computes the probability of a random correspondence (PRC) is derived based on the mixture models. A PRC of 2.25 times10-6 corresponding to 12 minutiae matches was computed for the NIST4 Special Database, when the numbers of query and template minutiae both equal 46. This is also the estimate of the PRC for a target population with a similar composition as that of NIST4.