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Fingerprint identification is based on two basic premises: (1) persistence and (2) individuality. We address the problem of fingerprint individuality by quantifying the amount of information available in minutiae features to establish a correspondence between two fingerprint images. We derive an expression which estimates the probability of a false correspondence between minutiae-based representations from two arbitrary fingerprints belonging to different fingers. Our results show that (1) contrary to the popular belief, fingerprint matching is not infallible and leads to some false associations, (2) while there is an overwhelming amount of discriminatory information present in the fingerprints, the strength of the evidence degrades drastically with noise in the sensed fingerprint images, (3) the performance of the state-of-the-art automatic fingerprint matchers is not even close to the theoretical limit, and (4) because automatic fingerprint verification systems based on minutia use only a part of the discriminatory information present in the fingerprints, it may be desirable to explore additional complementary representations of fingerprints for automatic matching.