Correct. This is the crux of the matter! The number of molecules per unit volume is proportional to the density of air (which is the mass of the air per unit volume). If the balloon is going to float, the density of air inside must be less than that outside (just like something floating in water must be less dense than the water it displaces). In fact, heating the air in the balloon must cause an amount of air molecules to leave the balloon such that their weight is greater than the total weight of the balloon and its payload. To find out how heating the balloon does this, click on the man in the basket.