This paper concerns the problem of agent trust in an electronic market place. We maintain that agent trust involves making decisions under uncertainty and therefore the phenomenon should be modelled probabilistically. We therefore propose a probabilistic framework that models agent interactions as a Hidden Markov Model (HMM). The observations of the HMM are the interaction outcomes and the hidden state is the underlying probability of a good outcome. The task of deciding whether to interact with another agent reduces to probabilistic inference of the current state of that agent given all previous interaction outcomes. The model is extended to include a probabilistic reputation system which involves agents gathering opinions about other agents and fusing them with their own beliefs. Our system is fully probabilistic and hence delivers the following improvements with respect to previous work: (a) the model assumptions are faithfully translated into algorithms; our system is optimal unde...