We present a semi-analytical formula to calculate the probability of finding
gravitational arcs in galaxy clusters being induced by their massive dark matter
haloes as a function of the cluster's redshifts and virial masses. The probabilities
are calculated and compared for two dark-matter halo proles, the Non-Singular-
Isothermal-Sphere (NSIS) and the Navarro, Frenk and White (NFW). We find
that for a sample of galaxy clusters a statistical analysis on the presence of strong
lensing for both cluster dark-matter models provide important restrictions on the
parameters dening the respective density proles. In particular, applying this
formulation to a prescribed sample of low redshift clusters, establishes limits
on the values of the core radius for the NSIS prole, and on the concentration
parameter for the NFW prole.