Determining Type Ia Supernovae Host galaxy extinction probabilities and
  a statistical approach to estimating the absorption-to-reddening ratio $R_V$
  We investigate limits on the extinction values of Type Ia supernovae to
statistically determine the most probable color excess, E(B-V), with
galactocentric distance, and use these statistics to determine the
absorption-to-reddening ratio, $R_V$, for dust in the host galaxies. We
determined pixel-based dust mass surface density maps for 59 galaxies from the
Key Insight on Nearby Galaxies: a Far-Infrared Survey with \textit{Herschel}
(KINGFISH, Kennicutt et al. (2011)). We use Type Ia supernova spectral
templates (Hsiao et al. 2007) to develop a Monte Carlo simulation of color
excess E(B-V) with $R_V$ = 3.1 and investigate the color excess probabilities
E(B-V) with projected radial galaxy center distance. Additionally, we tested
our model using observed spectra of SN 1989B, SN 2002bo and SN 2006X, which
occurred in three KINGFISH galaxies. Finally, we determined the most probable
reddening for Sa-Sap, Sab-Sbp, Sbc-Scp, Scd-Sdm, S0 and Irregular galaxy
classes as a function of $R/R_{25}$. We find that the largest expected
reddening probability are in Sab-Sb and Sbc-Sc galaxies, while S0 and
Irregulars are very dust poor. We present a new approach for determining the
absorption-to-reddening ratio $R_V$ using color excess probability functions,
and find for a sample of 21 SNe Ia observed in Sab-Sbp galaxies, and 34 SNe in
Sbc-Scp, an $R_V$ of 2.71 $\pm$ 1.58 and $R_V$ = 1.70 $\pm$ 0.38 respectively.
