  The reduced basis method is a powerful model reduction technique designed to
speed up the computation of multiple numerical solutions of parametrized
partial differential equations. We consider a quantity of interest, which is a
linear functional of the PDE solution. A new probabilistic error bound for the
reduced model is proposed. It is efficiently and explicitly computable, and we
show on different examples that this error bound is sharper than existing ones.
We include application of our work to sensitivity analysis studies.
