Question: 1. Suppose you play the venerable game rock-paper-scissors. If you pick paper and your opponent chooses arbitrarily, what is the probability that you will win? If each of you pick arbitrarily, what is the probability that you will win?
2. Suppose you play rock-paper-scissors and there is a draw (that is, both you and your opponent choose the same object). You decide to try to break the tie by playing again. What is the probability that you win in the second game, given that you reached a draw in the first game? What is the probability that you draw in the first game and win the second game?