Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of the three possibilities every round (independently of the other player and the previous choices). (a) What is the probability that Ann wins the first round? (Remember that the round could end in a tie.) (b) What is the probability that Ann’s first win happens in the fourth round? (c) What is the probability that Ann’s first win comes after the fourth round?