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We investigate limits on the extinction values of Type Ia supernovae tostatistically determine the most probable color excess, E(B-V), withgalactocentric distance, and use these statistics to determine theabsorption-to-reddening ratio, $R_V$, for dust in the host galaxies. Wedetermined pixel-based dust mass surface density maps for 59 galaxies from theKey Insight on Nearby Galaxies: a Far-Infrared Survey with \textit{Herschel}(KINGFISH, Kennicutt et al. (2011)). We use Type Ia supernova spectraltemplates (Hsiao et al. 2007) to develop a Monte Carlo simulation of colorexcess E(B-V) with $R_V$ = 3.1 and investigate the color excess probabilitiesE(B-V) with projected radial galaxy center distance. Additionally, we testedour model using observed spectra of SN 1989B, SN 2002bo and SN 2006X, whichoccurred in three KINGFISH galaxies. Finally, we determined the most probablereddening for Sa-Sap, Sab-Sbp, Sbc-Scp, Scd-Sdm, S0 and Irregular galaxyclasses as a function of $R/R_{25}$. We find that the largest expectedreddening probability are in Sab-Sb and Sbc-Sc galaxies, while S0 andIrregulars are very dust poor. We present a new approach for determining theabsorption-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 inSbc-Scp, an $R_V$ of 2.71 $\pm$ 1.58 and $R_V$ = 1.70 $\pm$ 0.38 respectively.

Determining Type Ia Supernovae Host galaxy extinction probabilities and a statistical approach to estimating the absorption-to-reddening ratio $R_V$