Low energy electron attachment to mixed (H$_2$)$_x$/(O$_2$)$_y$ clusters and their deuterated analogues has been investigated for the first time. These experiments were carried out using liquid helium nanodroplets to form the clusters, and the effect of the added electron was then monitored via mass spectrometry. There are some important differences between electron attachment to the pure clusters and to the mixed clusters. A particularly notable feature is the formation of HO$_2$$^{-}$ and H$_2$O$^{-}$ ions from an electron-induced chemical reaction between the two dopants. The chemistry leading to these anions appears to be driven by electron resonances associated with H$_2$ rather than O$_2$. The electron resonances for H$_2$ can lead to dissociative electron attachment (DEA), just as for the free H$_2$ molecule. However, there is evidence that the resonance in H$_2$ can also lead to rapid electron transfer to O$_2$, which then induces DEA of the O$_2$. This kind of excitation transfer has not, as far as we are aware, been reported previously