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Diagnostic testing is germane to a variety of scenarios in medicine, pandemic tracking, threat detection, and signal processing. This is an expository paper with some original results. Here we first set up a mathematical architecture for diagnostics, and explore its probabilistic underpinnings. Doing so enables us to develop new metrics for assessing the efficacy of different kinds of diagnostic tests, and for solving a long standing open problem in diagnostics, namely, comparing tests when their receiver operating characteristic curves cross. The first is done by introducing the notion of what we call, a Gini Coefficient; the second by invoking the information theoretic notion of dinegentropy. Taken together, these may be seen a contribution to the state of the art of diagnostics. The spirit of our work could also be relevant to the much discussed topic of batch testing, where each batch is defined by the partitioning strategy used to create it. However this possibility has not been explored here in any detail. Rather, we invite the attention of other researchers to investigate this idea, as future work.