Several models describing neutral particle transport through a binary stochastic background mixture are numerically compared. The test problem is one-group, time-independent transport with isotropic scattering in a source-free rod. The mixing statistics of the rod are taken as homogeneous and Markovian. Ensemble-averaged reflection and transmission probabilities as predicted by seven approximate models are compared with exact benchmark results that are available in the literature. Scalar flux plots that compare these seven models at interior rod locations are also given.