  In this paper we consider the stochastic dynamics of a finite system of
particles in a finite volume (Kac-like particle system) which annihilate with
probability $\alpha \in (0,1)$ or collide elastically with probability
$1-\alpha$. We first establish the well-posedness of the particle system which
exhibits no conserved quantities. We rigorously prove that, in some
thermodynamic limit, a suitable hierarchy of kinetic equations is recovered for
which tensorized solution to the homogenous Boltzmann with annihilation is a
solution. For bounded collision kernels, this shows in particular that
propagation of chaos holds true. Furthermore, we make conjectures about the
limit behaviour of the particle system when hard-sphere interactions are taken
into account.
