Water droplets can appear on the outer surface of a tumbler for several reasons:
Condensation: When the air surrounding the tumbler is humid and the temperature of the tumbler is lower than the dew point temperature of the air, water vapor in the air will condense on the surface of the tumbler. This is because the cooler tumbler causes the water vapor to reach its dew point and turn into liquid droplets.
Evaporation: If the tumbler contains a liquid, such as water or another beverage, and the temperature of the air surrounding the tumbler is lower than the boiling point of the liquid, the liquid will evaporate and form water vapor. If the air surrounding the tumbler is humid, the water vapor will condense on the surface of the tumbler and form droplets.
Leakage: If the tumbler has a crack or hole, liquid from inside the tumbler may leak out and form droplets on the outer surface of the tumbler.
Spilling: If the tumbler is tipped or turned over, any liquid inside the tumbler may spill out and form droplets on the outer surface of the tumbler.