DNA fingerprinting is a microbiological technique widely used to find a DNA sequence specific for a microbe. It involves slicing the genomes of the microbe into DNA fragments with manageable sizes, sorting the DNA pieces by length and finally identifying a DNA sequence unique to the microbe, using probe-based assays. This unique DNA is referred to as DNA fingerprint of the microbe under study. In this paper, we introduce a probabilistic model to estimate the chance of identifying the DNA fingerprint from the genome of a microbe when the DNA fingerprinting method is employed. We derive a closed-form functional relationship between the chance of finding the fingerprint and factors that can be experimentally controlled either in part, fully or not at all. Because the odds of finding a specific DNA fingerprint can only be improved by experimental design to a certain degree, in a broader sense, we show that the discovery of a DNA fingerprint is a process governed more by chance than by design. Nevertheless, the results can be potentially used to guide experiments in maximizing the chance of finding a DNA fingerprint of interest.