Here is an analysis on the frequency, number, distance, and probability of Earth-like planets (Earth-size within the habitable zone) around M-dwarf stars within 10 parsecs (~33 light years) from Earth. Table 1 shows these numbers for ηE (eta Earth) from four definitions of an Earth-like planet of Kopparapu (2013). These numbers assume that there are 248 M-dwarfs stars (RECONS) in 198 stellar systems (NSC) within 10 parsecs.
Table 1. Statistics of nearby Earth-like planets around M-dwarfs stars (see legend below for field definitions) for four definitions of Earth-like planet based on their size and orbit within a conservative or optimistic habitable zone.
ηE (eta Earth) = frequency of Earth-like planets per star (also called fraction or occurrence).
NE = number of Earth-like planets.
δE (delta Earth) = mean distance between stellar systems with Earth-like planets.
pE 10 ly = probability of an Earth-like planet within 10 light years from Earth.
dE 95% = distance from Earth for the 95% confidence level of an Earth-like planet.
In summary, there are over one-hundred Earth-like planets around M-dwarf stars within 10 parsecs from Earth. Just one or two are probably transiting (transiting probability of ~0.6-1.6%). This also means that there are over 67 to 134 billion Earth-like planets around low mass stars in our galaxy. Assuming that there are 200 to 400 billion stars in the Milky Way where 70% of those are low mass stars (0.1 to 0.8 solar masses) (Bochanski et al., 2010).
Bochanski, J. J., Hawley, S. L., Covey, K. R., West, A. A., Reid, I. N., Golimowski, D. A., and Ivezić, v. (2010). The Luminosity and Mass Functions of Low-mass Stars in the Galactic Disk. II. The Field. The Astronomical Journal, 139, 6, 2679.
Kopparapu, R. K. (2013). A Revised Estimate of the Occurrence Rate of Terrestrial Planets in the Habitable Zones around Kepler M-dwarfs. The Astrophysical Journal Letters, 767, 1, L8.