The stochastic Boolean satisfiability (SSAT) problem was introduced by Papadimitriou in 1985 by adding a probabilistic model of uncertainty to propositional satisfiability through
quantification. SSAT has many applications, e.g., in probabilistic planning and, more recently by integrating arithmetic, in probabilistic model checking. In this paper, we first present a new result on the computational complexity of SSAT: SSAT remains PSPACE-complete even for its restriction to 2CNF. Second, we propose a sound and complete resolution calculus for SSAT complementing the classical backtracking search algorithms.