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.
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