  This paper investigates the influences of standard numerical discretizations
on hitting probabilities for linear stochastic parabolic system driven by
space-time white noises. We establish lower and upper bounds for hitting
probabilities of the associated numerical solutions of both temporal and
spatial semi-discretizations in terms of Bessel-Riesz capacity and Hausdorff
measure, respectively. Moreover, the critical dimensions of both temporal and
spatial semi-discretizations turn out to be half of those of the exact
solution. This reveals that for a large class of Borel sets $A$, the
probability of the event that the paths of the numerical solution hit $A$
cannot converge to that of the exact solution.
