Fingerprint identification is based on two basic premises: (i) persistence: the basic characteristics of fingerprints do not change with time; and (ii) individuality: the fingerprint is unique to an individual. The validity of the first premise has been established by the anatomy and morphogenesis of friction ridge skin. While the second premise has been generally accepted to be true based on empirical results, the underlying scientific basis of fingerprint individuality has not been formally tested. As a result, fingerprint evidence is now being challenged in several court cases. We address the problem of fingerprint individuality by quantifying the amount of information available in minutiae points to establish a correspondence between two fingerprint images. We derive an expression which estimates the probability of falsely associating minutiae-based representations from two arbitrary fingerprints. For example, the probability that a fingerprint with 36 minutiae points will share 15 minutiae points with another arbitrarily chosen fingerprint with 36 minutiae points is 4:26 \times 10^-7. These probability estimates are compared with typical fingerprint matcher accuracy results. Our results show that (i) contrary to the popular belief fingerprint matching is not infallible and leads to some false associations, (ii) the performance of automatic fingerprint matcher does not even come close to the theoretical performance, and (iii) due to the limited information content of the minutiae-based representation, the automatic system designers should explore the use of non-minutiae-based information present in the fingerprints.