Yes, we can conclude that the water collected outside the tumbler is due to condensation, as the cold surface of the tumbler causes water vapor in the air to turn into liquid droplets.
Can we conclude that the water collected outside the tumbler is only due to condensation?
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Yes, we can conclude that the water collected outside the tumbler is due to condensation. The cooler tumbler surface causes moisture from the air to condense into water droplets, which gather on the outside of the tumbler.