  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 (HST) 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 eleven 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 (t(2)) of M31 novae, how the likely bulge and disk nova
distributions compare, and how the M31 t(2) distribution compares to that of
the Milky Way. Using a detailed Monte Carlo simulation, we determine that 30
(+13/-10) percent of all M31 nova eruptions can be attributed to RG-nova
systems, and at the 99 percent confidence level, >10 percent 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 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.
