The formulas can be used in determining the probabilities for the random occurrence of any sequence of striations and provide a straightforward way for the quantitative justification for the significance of a specific match between any two bullets. The development of a theoretical foundation for bullet comparisons, in accordance with matching particular sections of a land or groove impression, requires determining the number of times that a particular sequence of striations can occur on a random suspect bullet and dividing it into the total number of these patterns that actually exist on the subject bullet. This quantity is the probability that one of the patterns on the random bullet will match. This calculation multiplies the number of possible sequences on the subject bullet with the probability for finding a particular one of the sequences on a random suspect bullet in order to determine the likelihood that a match can occur by pure chance. Before these quantities can be determined, however, it is necessary to establish the maximum number of striations that can be accommodated on the land impression of the bullets. This first step requires an examiner to evaluate the surfaces of the two bullets at 30-40x magnification through a microscope. A calculation of the probabilities for finding pairs and triplets of consecutively matching lines on nonmatching bullets by an examiner with normal perception using a microscope at 40x magnification produces values that agree well with the empirical probabilities determined by Biasotti in the 1950s. 7 figures and 6 tables