  A search for previously unobserved decays of beauty baryons to the final
states $K^0_{\mathrm{S}}p\pi^-$ and $K^0_{\mathrm{S}}pK^-$ is reported. The
analysis is based on a data sample corresponding to an integrated luminosity of
$1.0\,\mathrm{fb}^{-1}$ of $pp$ collisions. The $\Lambda^0_b \rightarrow
K^0_{\mathrm{S}}p\pi^-$ decay is observed for the first time with a
significance of $8.6\,\sigma$, and a measurement is made of the $CP$ asymmetry,
which is consistent with zero. No significant signals are seen for $\Lambda^0_b
\rightarrow K^0_{\mathrm{S}}pK^-$ decays, $\Xi^0_b$ decays to both
$K^0_{\mathrm{S}}p\pi^-$ and $K^0_{\mathrm{S}}pK^-$ final states, and the
$\Lambda^0_b \rightarrow D^-_s (K^0_{\mathrm{S}}K^-)p$ decay, and upper limits
on their branching fractions are reported.
