We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context-Free Grammar G over alphabet Sigma , count the number of words of length exactly n generated by G 2. Given a circuit phi in Decomposable Negation Normal Form (DNNF) over the set of Boolean variables X , compute the number of assignments to X such that phi evaluates to 1. Finding polynomial time algorithms for the aforementioned problems has been a longstanding open problem. Prior work could either only obtain a quasi-polynomial runtime or a polynomial-time randomized approximation scheme for non-deterministic finite automata and non-deterministic tree automata.