To resolve ambiguity, a Probabilistic Context-Free Grammar (PCFG) calculates the probability of each possible parse tree (derivation) $T$ for a given sentence $S$. The joint probability of tree $T$ and sentence $S$ is defined as the product of the probabilities of all rules used in the derivation: P(T,S) = prod_{i=1}^{n} P(RHS_i | LHS_i). The PCFG then chooses the parse tree with the greatest probability as the correct parse of $S$.