First observation of the decay $bar{B}^0_s to D^0 K^{*0}$ and a measurement of the ratio of branching fractions $frac{{cal B}(bar{B}^0_s to D^0 K^{*0})}{{cal B}(bar{B}^0 to D^0 rho^0)}$

The first observation of the decay $bar{B}^0_s to D^0 K^{*0}$ using $pp$ data collected by the LHCb detector at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 36 pb$^{-1}$, is reported. A signal of $34.4 pm 6.8$ events is obtained and the absence of signal is rejected with a statistical significance of more than nine standard deviations. The $bar{B}^0_s to D^0 K^{*0}$ branching fraction is measured relative to that of $bar{B}^0 to D^0 rho^0$: $frac{{cal B}(bar{B}^0_s to D^0 K^{*0})}{{cal B}(bar{B}^0 to D^0 rho^0)} = 1.48 pm 0.34 pm 0.15 pm 0.12$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $B^0$ and $B^0_s$ hadronisation fractions.