Hydraulic failure of a funnel-and-gate system may occur when the contaminant plume bypasses the funnels rather than being captured by the gate. We analyze the uncertainty of capturing the plumes by funnel-and-gate systems in heterogeneous aquifers. Restricting the analysis to two-dimensional, steady state flow, we characterize plume capture by the values of the stream function at the boundaries of the plume and the funnels. On the basis of the covariance of the log conductivity distribution we compute the covariance matrix of the relevant stream function values by a matrix-based first-order second-moment method, making use of efficient matrix-multiplication techniques. From the covariance matrix of stream function values, we can approximate the probability that the plume is bypassing the funnels. We condition the log conductivity field to measurements of the log conductivity and the hydraulic head. Prior to performing additional measurements, we estimate their worth by the expected reduction in the variance of stream function differences. In an application to a hypothetical aquifer, we demonstrate that our method of uncertainty propagation and our sampling strategy enable us to discriminate between cases of success and failure of funnel-and-gate systems with a small number of additional samples.