  In this paper, we study the dynamics of a random walker diffusing on a
disordered one-dimensional lattice with random trappings. The distribution of
escape probabilities is computed exactly for any strength of the disorder.
These probabilities do not display any multifractal properties contrary to
previous numerical claims. The explanation for this apparent multifractal
behavior is given, and our conclusion are supported by numerical calculations.
These exact results are exploited to compute the large time asymptotics of the
survival probability (or the density) which is found to decay as $\exp
[-Ct^{1/3}\log^{2/3}(t)]$. An exact lower bound for the density is found to
decay in a similar way.
