The first observation of the decay mode and evidence for the decay mode are reported. The data sample corresponds to an integrated luminosity of 3.0 collected in collisions by LHCb at center-of-mass energies of 7 and 8 TeV. The branching fractions are measured to be \begin{align*} (B^0_s\to\bar{D}^0 \bar{K}^0) &= (4.3\pm0.5()\pm0.3()\pm0.3()\pm0.6())\times10^{-4},\ (B^0_s\to\bar{D}^{0} \bar{K}^0) &= (2.8\pm1.0()\pm0.3()\pm0.2()\pm0.4())\times10^{-4}, \end{align} where the uncertainties are due to contributions coming from statistical precision, systematic effects, and the precision of two external inputs, the ratio and the branching fraction of $B^0\to\bar{D}^0 K^0_S$, which is used as a calibration channel.

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