Parrondo's paradox concerns two games that are played in an alternating sequence. An analysis of each game in isolation shows them both to be losing games (i.e., to have a negative expectation). However, when the two games are played in an alternating sequence, the resulting compound game is, paradoxically, a winning game with a positive expectation. This paradox has aroused a great deal of interest in recent years, and a number of sophisticated resolutions of it have been published. It is the purpose of this article to show that the paradox is not paradoxical at all, and is easily resolved using elementary probability.