  The transport coefficients of a granular binary mixture driven by a
stochastic bath with friction are determined from the inelastic Boltzmann
kinetic equation. A normal solution is obtained via the Chapman-Enskog method
for states near homogeneous steady states. The mass, momentum, and heat fluxes
are determined to first order in the spatial gradients of the hydrodynamic
fields, and the associated transport coefficients are identified. They are
given in terms of the solutions of a set of coupled linear integral equations.
As in the monocomponent case, since the collisional cooling cannot be
compensated locally for by the heat produced by the external driving, the
reference distributions (zeroth-order approximations) $f_i^{(0)}$ ($i=1,2$) for
each species depend on time through their dependence on the pressure and the
temperature. Explicit forms for the diffusion transport coefficients and the
shear viscosity coefficient are obtained by assuming the steady state
conditions and by considering the leading terms in a Sonine polynomial
expansion. A comparison with previous results obtained for granular Brownian
motion and by using a (local) stochastic thermostat is also carried out. The
present work extends previous theoretical results derived for monocomponent
dense gases [V. Garz\'o, M. G. Chamorro, and F. Vega Reyes, Phys. Rev. E
\textbf{87}, 032201 (2013)] to granular mixtures at low density.
