  In this paper the random packing fraction of hard disks in a plane is
analyzed, following a geometric probabilistic approach. First, the random close
packing (RCP) of equally sized disks is modelled. Subsequently, following the
same methodology, a simple, statistical geometric model is proposed for the
random loose packing (RLP) of monodisperse disks. This very basic derivation of
RLP leads to a packing value (~ 0.66) that is in very good agreement with
values that have been obtained previously for 2D disk packings. The present
geometrical model also enables closed-form expression for the contact
(coordination) number as function of the packing density at different states of
compaction. These predictions are thoroughly compared with empirical and
simulation results, among others the R\'enyi parking model, yielding good
agreement.
