Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of rock, paper, and scissors every round (making independent selections each round). Each round can end in a win, loss, or a tie for each player.
What is the probability Ann wins the first round.? (Remember that a tie is a possibility.)Prob =
What is the probability that Ann's first win happens in round #3?Prob =
What is the probability that Ann's first win comes after round #3?Prob =