  The energy densities of dark matter (DM) and dark energy (DE) are of the same
order at the present epoch despite the fact that both these quantities have
contrasting characteristics and are presumed to have evolved distinctively with
cosmic evolution. This is a major issue in standard $\Lambda$CDM cosmology and
is termed "The Coincidence Problem" which hitherto cannot be explained by any
fundamental theory. In this spirit, Bisabr \cite{bisabr} reported a
cosmological scenario in $f(R)$ gravity where DM and DE interact and exchange
energy with each other and therefore evolve dependently. We investigate the
efficiency and model independancy of the technique reported in Bisabr
\cite{bisabr} in addressing the Coincidence problem with the help of two $f(R)$
gravity models with model parameters constrained from various observations. Our
result confirm the idea that not all scalar-tensor gravity theories and models
can circumvent the Coincidence Problem and any cosmological scenario with
interacting fluids is highly model dependent and hence alternate model
independent theories and ideas should be nominated to solve this mystery.
