In our preceding paper, Liverpool Telescope data of M31 novae in eruption were used to facilitate a search for their progenitor systems within archival Hubble Space Telescope data, with the aim of detecting systems with red giant secondaries (RG-novae) or luminous accretion disks. From an input catalog of 38 spectroscopically confirmed novae with archival quiescent observations, likely progenitors were recovered for 11 systems. Here we present the results of the subsequent statistical analysis of the original survey, including possible biases associated with the survey and the M31 nova population in general. As part of this analysis, we examine the distribution of optical decline times (t2) of M31 novae, how the likely bulge and disk nova distributions compare, and how the M31 t2 distribution compares to that of the Milky Way. Using a detailed Monte Carlo simulation, we determine that of all M31 nova eruptions can be attributed to RG-nova systems, and at the 99% confidence level, of all M31 novae are RG-novae. This is the first estimate of a RG-nova rate of an entire galaxy. Our results also imply that RG-novae in M31 are more likely to be associated with the M31 disk population than the bulge; indeed, the results are consistent with all RG-novae residing in the disk. If this result is confirmed in other galaxies, it suggests that any Type Ia supernovae that originate from RG-nova systems are more likely to be associated with younger populations and may be rare in old stellar populations, such as early-type galaxies.
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