  Monte Carlo (MC) simulations allowing to describe photons propagation in
statistical mixtures represent an interest that goes way beyond the domain of
optics, and can cover, e.g., nuclear reactor physics, image analysis or life
science just to name a few. MC simulations are considered a ``gold standard''
because they give exact solutions (in the statistical sense), however, in the
case of statistical mixtures they are enormously time consuming and their
implementation is often extremely complex. For this reason, the aim of the
present contribution is to propose a new approach that should allow us in the
future to simplify the MC approach. This is done through an explanatory
example, i.e.; by deriving the `exact' analytical expression for the
probability density function of photons' random steps (single step function,
SSF) propagating in a medium represented as a binary (isotropic-Poisson)
statistical mixture. The use of the SSF reduces the problem to an `equivalent'
homogeneous medium behaving exactly as the original binary statistical mixture.
This will reduce hundreds time-consuming MC simulations to only one equivalent
simple MC simulation. To the best of our knowledge the analytically `exact' SSF
for a binary (isotropic-Poisson) statistical mixture has never been derived
before.
