We consider semi-classical Schrödinger operators with potentials supported

in a bounded strictly convex subset O of Rⁿ with smooth boundary.

Letting h denote the semi-classical parameter, we consider classes

of small random perturbations and show that with probability very close

to 1, the number of resonances in rectangles [ a, b ] - i [0, ch 2/3], is equal to

the number of eigenvalues in [ a, b ] of the Dirichlet realization of the unperturbed

operator in O up to a small remainder.