If this was the case we could drink seawater on the off chance that it did not contain any sodium chloride. Hey presto, world water supply problem solved if sea water is potable.Posted by Dr Mas
Remember, according to probality law, it is quite possible that the 2nd starting material "drop" may not contain any molecule of 1st starting material (because that drop was picked up blindly from the 1st bottle) and it may or may not contain 50% of the 1st starting material or may contain 99% of the starting material. Hence, avogadro's law can be applied in the same manner as it was demonstrated by you (member) earlier.
Actually, the chemical potential (the thermodynamic driving force) for a concentration to become completely uniform throughout the solvent is all downhill (even without stirring or succession, whatever that is).