Three friends Alan, Roger and Peter attempt to answer a question on…

Three friends Alan, Roger and Peter attempt to answer a question on an exam. Alan randomly guesses the answer, giving him a 1/5 probability of guessing correctly. Roger cheats by looking at the paper of the student in front of him, giving him a 2/3 probability of answering correctly. And Peter dutifully performs the calculations, then marks the answer, giving him a 5/6 probability of a correct answer. What is the probability that the question is answered correctly, but not via cheating?

AQuA-RAT — Algebra Question Answering with Rationales (Ling et al., DeepMind, 2017) · test #200