  We show the existence of a self-similar solution for a modified Boltzmann
equation describing probabilistic ballistic annihilation. Such a model
describes a system of hard-spheres such that, whenever two particles meet, they
either annihilate with probability $\alpha \in (0,1)$ or they undergo an
elastic collision with probability $1 - \alpha$. For such a model, the number
of particles, the linear momentum and the kinetic energy are not conserved. We
show that, for $\alpha$ smaller than some explicit threshold value $ \alpha_*$,
a self-similar solution exists.
