As a chemist I'd say that the question is really impossible to answer as given.
The gist is that for a water/ethanol mixture both components will evaporate. So if the liquid is left out long enough, the liquid will evaporate completely.
The atmosphere contains essentially no ethanol so an equilibrium between the whole atmosphere and the ethanol in a glass can never be reached. There is water in the atmosphere (aka humidity) so the evaporation of water could be retarded, or prevented entirely if the "local" humidity is 100%. But unless the "local" humidity is already 100% then an equilibrium between the liquid and the atmospheric water won't be reached either.
Pure ethanol has a higher vapor pressure and thus evaporates faster than pure water (in 0% humidity). So the gist is that as liquid evaporates the water/ethanol composition of the liquid will change. Thus the relative rate of evaporation of water and ethanol changes too.
In terms of the rate of evaporation there are a number of unspecified parameters.
How much volume compared to the exposed surface area? So liquid will evaporate more slowly from a tall narrow glass than a short wide one.
Temperature? The higher the temperature the faster the evaporation.
Air currents? If you use a fan to blow air across the glass evaporation will occur much faster than if a fan isn't used.