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Software architectures of large-scale systems are perceptibly shifting towards employing open and distributed computing. Service Oriented Computing (SOC) is a typical example of such environment in which the quality of interactions amongst software agents is a critical concern. Agent-based web services in open and distributed architectures need to interact with each other to achieve their goals and fulfill complex user requests. Two common tasks are influenced by the quality of interactions among web services: the selection and composition. Thus, to ensure the maximum gain in both tasks, it is essential for each agent-based web service to maintain a model of its environment. This model then provides a means for a web service to predict the quality of future interactions with its peers. In this paper, we formulate this model as a machine learning problem which we analyze by modeling the trustworthiness of web services using probabilistic models. We propose two approaches for trust learning of single and composed services; Bayesian Networks and Mixture of Multinomial Dirichlet Distributions (MMDD). The effectiveness of our approaches is empirically assessed using a simulation study. Our results show that representing the quality of a web service by Multinomial Dirichlet Distribution (MDD) provides high flexibility and accuracy in modeling trust. They also show that using our approaches to estimate trust enhances web services selection and composition.