  We assess the occurrence of fast neutrino flavor instabilities in two
three-dimensional state-of-the-art core-collapse supernova simulations
performed using a two-moment three-species neutrino transport scheme: one with
an exploding 9$\mathrm{M_{\odot}}$ and one with a non-exploding
20$\mathrm{M_{\odot}}$ model. Apart from confirming the presence of fast
instabilities occurring within the neutrino decoupling and the supernova
pre-shock regions, we detect flavor instabilities in the post-shock region for
the exploding model. These instabilities are likely to be scattering-induced.
In addition, the failure in achieving a successful explosion in the heavier
supernova model seems to seriously hinder the occurrence of fast instabilities
in the post-shock region. This is a consequence of the large matter densities
behind the stalled or retreating shock, which implies high neutrino scattering
rates and thus more isotropic distributions of neutrinos and antineutrinos. Our
findings suggest that the supernova model properties and the fate of the
explosion can remarkably affect the occurrence of fast instabilities. Hence, a
larger set of realistic hydrodynamical simulations of the stellar collapse is
needed in order to make reliable predictions on the flavor conversion physics.
