ROCK-PAPER-SCISSORS

Purpose

Explore the relationship between experimental and theoretical probabilities by introducing the concept of a fair game. We use a matrix and a tree diagram as tools.

Materials Needed: None

Procedure: Form groups of three (In the two-player game, one student records while the other two play the game.)

The two-player game is played as follows:

  • Each player makes a fist.
  • On the count of three, each player shows one of the following: scissors by showing two fingers, paper by showing four fingers, or rock by showing a fist.
  • If scissors and paper are shown, the player showing scissors wins, since the scissors cut paper.
  • 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 you both show the same, then it’s a tie.
  1. Do you think the game is fair? Why or why not?
  1. Play the game 45 times. Tally the outcomes in the table below:

Outcomes / Tally / Frequency
You Win
Partner Wins
Tie
  1. Does the game seem fair? What does “fair” mean from a probability perspective?

Probabilities Using a Matrix

You can determine if the game is fair without conducting an experiment.

Complete the matrix below.

  1. If the players randomly choose their handshapes,each of the nine outcomes in the matrix are equallylikely. Find the following probabilities in this case.

player B
A = / A Wins / Scissor / paper / Rock
B = / B Wins
T = / Tie
player A / Scissor / T
Paper / A
Rock

P(A wins) = ______

P(Bwins) = ______

P(Tie) = ______

  1. Based on the probabilities in #4, is this a fair game? Explain your reasoning.

Probabilities Using a Tree Diagram

Since Paper-Scissors-Rock can be thought of as a multi-stage experiment, it can also be analyzed using a tree diagram. Note: P=Paper, S=Scissors, and R=Rock. Complete the tree diagram below.

Player A Player B Outcome

P PP

P ______

______

______

S ______

______

______

R ______

______

Use the tree diagram to answer the following questions:

  1. What does the outcome PP mean? ______
  1. P(PS) = ______
  1. P(SP or SR) = ______
  1. P(A wins) = ______
  1. P(B wins) = ______
  1. P(at least one player shows scissors) = ______

A New Game- Rock, Paper, Scissors for Three

The three-player game is played as follows:

  • Decide which student is Player A, which one is Player B, and which one is Player C.
  • If all three players make the same hand shape, Player A gets a point.
  • If all three players make different hand shapes, Player B gets a point.
  • If two players make the same hand shape and one makes a different shape, Player C gets a point.

Play the game 45 times and tally the results in the table below:

Outcome / Tally / Frequency
A Wins
B Wins
C Wins
  1. Is this a fair game? Explain your answer.
  1. If you wanted to win this game, which player would you choose to be?
  1. Compare and contrast the two games (three-player versus the two-player)?
  1. Rewrite the rules for this game, so that it incorporates ties. Your group should decide what constitutes a tie and wins for players A, B, and C. Record your rules below:

Player A wins if ______

Player B wins if______

Player C wins if ______

Tie occurs if______

  1. Using your new rules, play the game 45 times and tally the results in the table below:

Outcome / Tally / Frequency
A Wins
B Wins
C Wins
Tie
  1. Is this a fair game? Explain your answer.
  1. Find the following probabilities:
  1. P( Player A wins) = ______
  1. P( Player B wins) = ______
  1. P( Player C wins) = ______
  1. P(Tie) = ______

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