Abstract: A fundamental question in science is how investigators are to convert their observations of the universe into information about the universe. That question is answered best using the language of probability theory. Using that language, what one expects to observe in any situation is given by the expectation value of the observable function with weight conditioned on the information one has accumulated. Before any observations have been reported, one must set the stage by defining the geometry of the parametric manifold. Because the observable must be expressed as a function to be evaluated mathematically, all models for the universe necessarily are parametric, even those which claim to be parameter free. As a concrete example of the process, a detailed study is made here of the simple problem of assigning a binary type to objects as they cross some specified line in space. The stage is set using the transformation group approach to establish the prior state of knowledge, and how one establishes the reliability of one’s predictive power is expressed. When the probabilistic nature of observation is respected, one realizes that even perfect knowledge of the likelihood of an event’s occurrence cannot yield perfect predictions of its occurrence, because the action of observation amounts to the selection of one particular universe out of the many which are possible.