  Noisy scattering dynamics in the randomly driven H\'enon-Heiles system is
investigated in the range of initial energies where the motion is unbounded. In
this paper we study, with the help of the exit basins and the escape time
distributions, how an external perturbation, be it dissipation or periodic
forcing with a random phase, can enhance or mitigate the unpredictability of a
system that exhibit chaotic scattering. In fact, if basin boundaries have the
Wada property, predictability becomes very complicated, since the basin
boundaries start to intermingle, what means that there are points of different
basins close to each other. The main responsible of this unpredictability is
the external forcing with random phase, while the dissipation can recompose the
basin boundaries and turn the system more predictable. Therefore, we do the
necessary simulations to find out the values of dissipation and external
forcing for which the exit basins present the Wada property. Through these
numerical simulations, we show that the presence of the Wada basins have a
specific relation with the damping, the forcing amplitude and the energy value.
Our approach consists on investigating the dynamics of the system in order to
gain knowledge able to control the unpredictability due to the Wada basins.
