Numerous variants of Kahneman and Tversky's (1972) hospital problem have been used to investigate intuitions about the Empirical Law of Large Numbers (eLLN). A largely separate line of research has focused on interactions between context knowledge and statistical reasoning. The present study merges these two lines of research by analyzing tertiary students' reasoning about a hospital problem variant set in a provocative context from their academic major. Participants' reasoning structures were diagrammed and compared against one another. Some responses closely matched an anticipated argument structure, and others differed along dimensions such as syllogistic structure, types of justifications offered, and task interpretation. Results of the study illustrate the importance of going beyond the metric of participants' success rate choosing the intended sample when doing research with contextually provocative hospital problem variants. Analyses of responses to such variants can be enhanced by examining the depth of eLLN intuition they reflect, their underlying syllogistic structures, and the extent to which application of the eLLN is qualified as needed in a given context.