In this research, the probability of misclassification error of a multilayer neural network used in binary-to-binary mappings is derived. The connection weights, determined through training, are assumed to be subject to an additive, random, normally distributed error. The probability of misclassification is also derived through simulation of example application. The simulation results and the theoretical results are shown to match very closely. Our results and the theoretical results are shown to match closely. Our results give predictability to NN performance and allow for changing NN design parameters, such as weight vectors and number of nodes, in order to obtain a certain tolerance to weight errors.