Use a probability tree to solve the following problem.

At the end of each class, Prof. McTreeville picks a student and asks them a multiple-choice question with the options A, B, and C. She allows the student to ask whether their answer is right or wrong before they make their final decision. Prof. McTreeville may respond to this question in one of two ways: she can either say "your answer is wrong" or "I can't tell you the answer." Assume that Prof. McTreeville never lies to her students, that is, she never tells them their answer is wrong when it isn't. Assume that if a student's 1 answer is wrong, Prof. McTreeville responds with "your answer is wrong" or "I can't tell you the answer" with equal probabilities. Laura guesses answer A, and asks Prof. McTreeville whether her answer is right. Prof. McTreeville says: "I can't tell you the answer." Assuming that Laura has no other relevant information, should she keep her answer A, or should she change it to B or C?