  Using the observed rate of short-duration gamma-ray bursts (GRBs) it is
possible to make predictions for the detectable rate of compact binary
coalescences in gravitational-wave detectors. These estimates rely crucially on
the growing consensus that short gamma-ray bursts are associated with the
merger of two neutron stars or a neutron star and a black hole, but otherwise
make no assumptions beyond the observed rate of short GRBs. In particular, our
results do not assume coincident gravitational wave and electromagnetic
observations. We show that the non-detection of mergers in the existing
LIGO/Virgo data constrains the progenitor masses and beaming angles of
gamma-ray bursts. For future detectors, we find that the first detection of a
NS-NS binary coalescence associated with the progenitors of short GRBs is
likely to happen within the first 16 months of observation, even in the case of
a modest network of observatories (e.g., only LIGO-Hanford and LIGO-Livingston)
operating at modest sensitivities (e.g., advanced LIGO design sensitivity, but
without signal recycling mirrors), and assuming a conservative distribution of
beaming angles (e.g. all GRBs beamed at \theta=30 deg). Less conservative
assumptions reduce the waiting time until first detection to weeks to months.
Alternatively, the compact binary coalescence model of short GRBs can be ruled
out if a binary is not seen within the first two years of operation of a
LIGO-Hanford, LIGO-Livingston, and Virgo network at advanced design
sensitivity. We also demonstrate that the rate of GRB triggered sources is less
than the rate of untriggered events if \theta<30 deg, independent of the noise
curve, network configuration, and observed GRB rate. Thus the first detection
in GWs of a binary GRB progenitor is unlikely to be associated with a GRB.
