Human activity recognition plays an important role especially in medical applications. This paper proposes a formal approach to model such activities, taking into account possible variations in human behavior. Starting from an activity description enriched with event occurrence probabilities, we translate it into a corresponding formal model based on discrete-time Markov chains (DTMCs). We use the PRISM framework and its model checking facilities to express and check interesting temporal logic properties concerning the dynamic evolution of activities. We illustrate our approach with the models of several serious games used by clinicians to monitor Alzheimer patients. We expect that such a modeling approach could provide new indications for interpreting patient performances. This paper addresses the definition of patient's models for three serious games and the suitability of this approach to check behavioral properties of medical interest. Indeed, this is a mandatory first step before clinical studies with patients playing these games. Our goal is to provide a new tool for doctors to evaluate patients.