Several important fluvial bedrock erosion processes are driven by the impact of bed load particles. Bed load transport rates fluctuate strongly in both nature and experiment, and stochastic models of the transport processes have been put forward to describe this behavior. In this paper I adapt a model based on a Markov chain formulation to derive probability distributions for bed load transport rate over a rock bed only partly covered by sediment. I propose a way to calculate the probability distribution of bed cover for given sediment supply using a combinatoric model and combine the two curves to calculate probability distributions for bed cover and erosion rate at constant hydraulics. In the proposed model, mean bed cover is an exponentially declining function of the number of particles in the control volume. The model describes recently published experimental data well, but at the moment it is not possible to finally discriminate between the exponential and the previously proposed linear model formulation. Distributions of erosion rate are fairly broad functions slightly skewed toward high erosion rates.