The possibility of observing binary in-spirals is one of the most promising features of planned LIGO/VIRGO interferometric gravitational wave detectors. This fascination derives partly from the fact that the luminosity distance to a merging binary is a direct observable quantity easy to obtain from the waveforms. Moreover, the intrinsic quantities of the binary system such as chirp mass, for example, are observed as multiplied by a factor involving the redshift of the source. This opens an intriguing possibility of accurate measurements of cosmological parameters like the Hubble constant. It turns out that the detection rate and a limiting redshift are crucial observables for this purpose. In advance of true experimental data following the start of LIGO/VIRGO observations we perform a theoretical experiment addressing the question of what we could expect for the Hubble constant, assuming that the gamma-ray bursts (GRBs) originate from neutron star binary mergers at cosmological distances in an Einstein-de Sitter universe. One can then perform a thought experiment imagining a fictitious gravitational wave detector, which registers in-spiral events with the same yearly rate and reaching the same maximal redshift as the Compton GRO (or other gamma-ray experiments), detecting the GRBs. In this thought experiment assuming 1.4-M_solar coalescing neutron stars a Hubble constant in the range of h=0.45-0.54x100 km s^-1 Mpc^-1 would be found. Evolution of the sources and luminosity function effects are also briefly discussed.