  We determine the asymptotic behavior of the tails of the steady state
velocity distribution of a homogeneously driven granular gas comprising of
particles having a scalar velocity. A pair of particles undergo binary
inelastic collisions at a rate that is proportional to a power of their
relative velocity. At constant rate, each particle is driven by multiplying its
velocity by a factor $-r_w$ and adding a stochastic noise. When $r_w <1$, we
show analytically that the tails of the velocity distribution are primarily
determined by the noise statistics, and determine analytically all the
parameters characterizing the velocity distribution in terms of the parameters
characterizing the stochastic noise. Surprisingly, we find logarithmic
corrections to the leading stretched exponential behavior. When $r_w=1$, we
show that for a range of distributions of the noise, inter-particle collisions
lead to a universal tail for the velocity distribution.
