Probability density function (grey histograms) of astrometric parameters and required radial velocities that result in a minimum separation of less than 10 pc between B1929+10/ζ Oph and B2020+28/B2021+51. Columns from left to right show the results for μ_α,μ_δ,π,and V_rad. For the measured parameters μ_α,μ_δ, andπ, the solid lines indicate the input parameter distributions derived from assuming Gaussian errors. The solid line in the last column indicates the input distribution for V_rad as derived from our measured transverse velocity and the empirically determined space velocity distribution derived by Hobbs et al. (2005). Objects from top to bottom are B1929+10, ζ Oph, B2020+28, and B2021+51.