The main objective of this article is to contribute to the limited research on teachers' knowledge of probability. In order to meet this objective, we presented prospective mathematics teachers with a variation of a well known task and asked them to determine which of five possible coin flip sequences was least likely to occur. To analyze particular normatively incorrect responses we utilized a brand new lens -- the composition fallacy -- instead of the traditional lenses and models associated with heuristic and informal reasoning about probability. In our application of the new lens we were able to determine that fallacious reasoning, not just heuristic reasoning, can account for normatively incorrect responses to the task. Given the success of the new lens, we contend that logical fallacies are a potential avenue for future investigations in comparisons of relative likelihood and research in probability in general. [For the complete proceedings, see ED585874.]