Decision making in water resources management usually requires the quantification of uncertainties. Monte Carlo techniques are suited for this analysis but imply a huge computational effort. An alternative and computationally efficient approach is the first-order second-moment (FOSM) method which directly propagates parameter uncertainty into the result. We apply the FOSM method to both the groundwater flow and solute transport equations. It is shown how conditioning on the basis of measured heads and/or concentrations yields the principle of interdependent uncertainty that correlates the uncertainties of feasible hydraulic conductivities and recharge rates. The method is used to compute the uncertainty of steady state heads and of steady state solute concentrations. It is illustrated by an application to the Palla Road Aquifer in semiarid Botswana, for which the quantification of the uncertainty range of groundwater recharge is of prime interest. The uncertainty bounds obtained by the FOSM method correspond well with the results obtained by the Monte Carlo method. The FOSM method, however, is much more advantageous with respect to computational efficiency. It is shown that at the planned abstraction rate the probability of exceeding the natural replenishment of the Palla Road Aquifer by overpumping is 30%.