  The star formation history and the internal dynamics of Milky Way satellite
galaxies are often complicated. In the last years, a substantial fraction of
the known faint dwarf satellites have been studied. Some of them show embedded
stellar substructures, such as star clusters and even globular star clusters.
In this work we study Eridanus II, a dwarf spheroidal satellite which hosts a
star cluster, using published and archival data from the Hubble Space Telescope
Advanced Camera for Surveys. We employ a Bayesian hierarchical method to infer
the star formation history of Eridanus II. We find that the bulk of the stars
in Eridanus II are very old ($13.5_{-1}^{+0.5}$ Gyr) and quite metal poor
($Z$\,=\,$0.00001$). We do not find any evidence of the presence of an
intermediate age or young population in Eri II. We cannot date the embedded
star cluster as a separate entity, but we find it likely that the cluster has a
similar age and metallicity as the bulk of the stars in Eri II.
  The existence of an old star cluster in a dark matter dominated old metal
poor dwarf galaxy is of major importance to cast light on the dark matter
distribution within dwarf galaxies. The existence of intermediate age stars is
required by the recent detection of carbon stars in Eri II. Since no recent
star formation is detected, {\it blue-straggler} fusions of lower mass stars
are the most likely origin of the carbon star progenitors.
