  This paper investigates the density of hypersurfaces in a projective normal
simplicial toric variety over a finite field having a quasismooth intersection
with a given quasismooth subscheme. The result generalizes the formula found by
B. Poonen for smooth projective varieties. As an application, we further
analyze the density of hypersurfaces with bounds on their number of
singularities and on the length of their singular schemes.
