Apples and Oranges

In front of you are three boxes, the first labelled ‘apples’, the second ‘oranges’ and the third ‘apples and oranges’. One box contains apples, one contains oranges, and the other contains apples and oranges. Each label, however, is on the wrong box. Your job is to correctly reassign the labels. You can’t see (or smell) what’s in any of the boxes. But you are allowed to stick your hand in one of them and remove a single piece of fruit.
Which box do you choose, and once you see that piece of fruit how do you deduce the correct contents of all the boxes?

(Source: Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles by Alex Bellos)

Take a fruit from the box labeled "apples and oranges". That box is to be labeled with the sign bearing the name of that fruit. If the first labeled box contains apples then the other two are currently labeled "apples" and "oranges". The box labeled "apples" contains oranges and the box labeled "oranges" contains apples and oranges. If however the first labeled box contains oranges then the box labeled "apples" contains apples and oranges and the box labeled "oranges" contains "apples and oranges".