Question

give a reason why water droplets appear on the surface of a tumbler containing ice water

Answer 1

that's because the tumbler is surrounded by the air outside the tumbler and due to low temperature inside the tumbler the outside water vapour or air condenses and sticks to the tumbler thus we see water droplets on the surface of the tumbler containing ice water

Answer 2

Water vapour present in air, comes in contact with the cold outside surface of the container there by condensing it to form water droplets.