Notas: Multimodal distribution functions that result froM Monte Carlo simulations can be interpreted by superimposing joint probability deNsity functions onto the countor space of the simulated calculations . The method is demostrated by analysis of the pathway of a radioactive ground water contaminant using an analytical solution to the transport equation . Simulated concentration at a fixed time and distance produce multimodal histograms , which are understood with reference to the parameter space for the two random variables - velocity and dispersity. Numerical integration under the joint density function up to the cotour of the analytical solution gives the probability of contaminant exceeding a target concentration . This technique is potentially more efficient than Monte Caro simulation for low probability events . Nevertheless, analyzing the two most pertinent random variables in a simulation might still offer insights into the multimodal nature of output histograms