  Based on the scenario that a $\bar{K} N N$ bound state is generated and it
eventually decays into $\Lambda p$, we calculate the cross section of the
$K^{-} {}^{3} \text{He} \to \Lambda p n$ reaction, which was recently measured
in the J-PARC E15 experiment. We find that the behavior of the calculated
differential cross section $d ^{2} \sigma / d M_{\Lambda p} d q_{\Lambda p}$,
where $M_{\Lambda p}$ and $q_{\Lambda p}$ are the $\Lambda p$ invariant mass
and momentum transfer in the $(K^{-} , \, n)$ reaction in the laboratory frame,
respectively, is consistent with the experiment. Furthermore, we can reproduce
almost quantitatively the experimental data of the $\Lambda p$ invariant mass
spectrum in the momentum transfer window $350 \text{ MeV} /c < q_{\Lambda p} <
650 \text{ MeV} /c$. These facts strongly suggest that the $\bar{K} N N$ bound
state was indeed generated in the J-PARC E15 experiment.
