Milk and coffee
This simple thought experiment has surprising result. The variation is a good activity for students to try to get a handle on the problem.
An 8-ounce cup of coffee and an 8-ounce cup of milk are sitting side by side. You take a tablespoon of milk and stir it into the coffee. Then you take a tablespoon of the mix and stir it back in the milk. Is there more milk in the coffee or coffee in the milk?
Divide up a standard deck of 52 playing cards into 26 red and 26 black. Then take any 5 red cards from the red half and put them in the black half. Now shuffle the (mostly) black pile, completely mixing in the red cards. Now take any 5 cards from the (mostly) black pile, and put them in the red pile. Are there more black cards in the red pile or red cards in the black pile? Does it matter how well you shuffled?
Alternatively, 10 red cards and 10 black cards could be used, moving 3 cards back and forth. What are the possibilities?