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We develop a model of parametric probabilistic transition systems. In this model probabilities associated with transitions may be parameters, and we show how to find instances of parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a given state. We show, as an application, the model of a probabilistic non repudiation protocol. The theory we develop, allows us to find instances that maximize the probability that the protocol ends in a fair state (no participant has an advantage over the others).