This paper addresses the challenge of truth discovery from noisy social sensing data. The work is motivated by the emergence of social sensing as a data collection paradigm of growing interest, where humans perform sensory data collection tasks. A challenge in social sensing applications lies in the noisy nature of data. Unlike the case with well-calibrated and well-tested infrastructure sensors, humans are less reliable, and the likelihood that participants' measurements are correct is often unknown a priori. Given a set of human participants of unknown reliability together with their sensory measurements, this paper poses the question of whether one can use this information alone to determine, in an analytically founded manner, the probability that a given measurement is true. The paper focuses on binary measurements. While some previous work approached the answer in a heuristic manner, we offer the first optimal solution to the above truth discovery problem. Optimality, in the sense of maximum likelihood estimation, is attained by solving an expectation maximization problem that returns the best guess regarding the correctness of each measurement. The approach is shown to outperform the state of the art fact-finding heuristics, as well as simple baselines such as majority voting.