[en] The time-independent linear transport problem in a purely absorbing (no scattering) random medium is considered. A formally exact equation for the ensemble averaged distribution function < Psi> is derived. Under the assumption of a two-fluid statistical mixture, with the transition from one fluid to the other assumed to be determined by a Markov process, an exact solution to this equation for < Psi> is obtained. In the source-free case, this solution is shown to agree with the result obtained by ensemble averaging simple exponential attenuation. Several approximations to the exact equation for < Psi> are considered, and numerical results given to assess the accuracy of these approximations