  We investigate the frequency and origin of carbon-enhanced metal-poor (CEMP)
stars in Local Group dwarf galaxies by means of a statistical, data-calibrated
cosmological model for the hierarchical build-up of the Milky Way and its dwarf
satellites. The model self-consistently explains the variation with dwarf
galaxy luminosity of the observed: i) frequency and [Fe/H] range of CEMP stars;
ii) metallicity distribution functions; iii) star formation histories. We show
that if primordial faint supernovae dominated the early metal enrichment, then
CEMP-no stars enriched by the first stellar generations should be present in
all dwarf galaxies, with similar number of stars and CEMP fractions at [Fe/H]$<
-4$. We demonstrate that the probability to observe a star that is
carbon-enhanced within a given [Fe/H] range strongly depends on the luminosity
of the dwarf galaxy and, on average, it is an order of magnitude lower in
"classical" Sculptor-like dSph galaxies ($P\leq 0.02$) than in the least
luminous ultra-faint dwarfs ($P \approx 0.1$). In addition, we explain why it
may be easier to find CEMP-no stars at [Fe/H]$\approx -2$ in classical dSph
galaxies than in ultra-faint dwarfs. These are consequences of the dramatic
variation in the fraction of stars at [Fe/H]$<-3$ with galaxy luminosity: $\geq
40\%$ for galaxies with $L<10^5L_{\odot}$, and $\leq 0.2\%$ for
$L>10^{7}L_{\odot}$. We present model predictions for the low Fe-tail and CEMP
fraction of stars in dwarf galaxies, with particular emphasis on the Sculptor
dSph, that can be used to shed light on the properties of the first stars.
