We study stochastic radiation transport through random media in one dimension, in particular for pure absorbing cases. The statistical model to calculate the ensemble-averaged transmission for a binary random mixture is derived based on the cumulative probability density function (PDF) of optical depth, which is numerically simulated for both Markovian and non-Markovian mixtures by Monte Carlo calculations. We present systematic results about the influence of mixtures' stochasticity on the radiation transport. It is found that mixing statistics affects the ensemble-averaged intensities mainly due to the distribution of cumulative PDF at small optical depths, which explains well why the ensemble-averaged transmission is observed to be sensitive to chord length distribution and its variances. The effect of the particle size is substantial when the mixtures' correlation length is comparable to the mean free path of photons, which imprints a moderately broad transition region into the cumulative PDF. With the mixing probability increasing, the intensity decreases nearly exponentially, from which the mixing zone length can be approximately estimated. The impact of mixed configuration is also discussed, which is in line with previous results.