Under Oath I

Question

Alice and Bob are witnesses to a crime. When asked questions, Alice and Bob respectively tell the truth with probability $p_A$ and $p_B$ (and lie with respective probabilities $1-p_A$ and $1-p_B$). The detective asks Alice a question, she gives an answer, and Bob confirms the answer given by Alice is truthful. Find the probability that Alice told the truth when $p_A = 1/3$ and $p_B = 3/5$.