10 Chapter 1: Probability Rock-Paper-Scissors Shoot! OBJECTIVES: Introduce the use of a matrix to find experimental probabilities and a tree diagram to calculate theoretical probabilities.' Reinforce fair games and use a matrix to find theoretical probabilities. MATERIALS: Pencil and a partner. INSTRUCTIONS: The rock-paper-scissors game has been popular for many years. The rules for the two-player game are as follows: Each player makes a fist. On the count of three, each player shows either scissors by showing two fingers, paper by showing an open hand, or rock by showing a fist. If scissors and paper are shown, the player showing scissors wins, since the scissors cut papers. If scissors and rock are shown, the player showing rock wins, since a rock breaks the scissors. If paper and rock are shown, the player showing paper wins, since paper wraps a rock. If both players show the same hand, there is a tie. Probabilities Using a Matrix 1. Do you think rock-paper-scissors is a fair game? Explain. 2. Play the game 45 times. Use the following matrix to tally the outcomes. Your Partner Rock Paper Scissors Rock You Paper Scissors 3. Use the data in your matrix to calculate the following experimental probabilities. P(you win) = P(your partner win) = P(tie) = 4. Use the probabilities in Question 3 to decide whether rock-paper-scissors is a fair game. Explain your reasoning. Mathematics Activity Book II: Learning and Teaching Escobar, Leticia