= Solution
Treat the quoted distances as sharp isotropic detection radii in a homogeneous Euclidean population. With galaxy <number density> $n_g$, the number surveyed is $N_g=(4\pi/3)n_gD^3$. One event per year requires a per-galaxy merger rate $\mathcal R=1/N_g$ per year. Thus
$$
\boxed{\begin{array}{c|r|l}
\text{pair}&N_g&\mathcal R\ (\mathrm{yr^{-1}\,galaxy^{-1}})\\\hline
\mathrm{NS+NS}&6.79\times10^5&1.47\times10^{-6}\\
\mathrm{NS+BH}&6.90\times10^6&1.45\times10^{-7}\\
\mathrm{BH+BH}&1.23\times10^8&8.10\times10^{-9}
\end{array}}
$$
The larger <gravitational wave> range gives enormous volume leverage: even a rare merger in a typical galaxy can yield frequent detections across the surveyed population. This supports promising detection prospects if astrophysical rates exceed these thresholds. The estimate is not a prediction of the rates themselves. Real sensitivity depends on sky direction, binary inclination, detector duty cycle and a signal-to-noise selection function; a quoted horizon distance is not automatically a volume-averaged range. Cosmological volume and source-time corrections also matter toward the largest quoted distance. The calculation follows the simple assumptions specified by the paper.
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