Genomic fingerprinting methods are useful in determining relatedness among bacterial strains. However, random coincidences in sizes of two DNA fragments in two different fingerprints may occur, resulting in erroneous interpretation of relatedness between two bacterial genomes. In this study, I estimated the probability of occurrence of DNA bands of identical size in fingerprints of two unrelated genomes, so that the significance of fingerprint-based estimation of genome relatedness could be analyzed. The probability could be estimated as outputs of a function formulated with the three parameters: the numbers of observed fragments, all possible sizes of fragments and observed fragments common in a given pair of fingerprints. The parameter most instrumental to significance of relatedness estimation was the number of all possible sizes of fragments. To keep the number of coincidentally-common size of fragments below 10, about 200 fragments should be distinguishable in the fingerprints.