Overview
In this task, students will play the game “Is It Fair?” in groups and record their information. Students will then use probability to determine whether they feel the game is fair or not. Predictions should be made before the game begins. Based on their trials, students will then determine all outcomes and create tree diagrams. Finally, students will determine the theoretical chance of winning for each player.
Illustrative Task
Game 1
Directions: Put a red-red and a red-yellow chip in a cup. Take turns shaking and tossing the chips. Player A scores a point if both chips land with the red side up. Player B gets a point if one of each color lands up. The first player with ten points wins the game.
| Player A gets 1 point. | | Player B gets 1 point. |
Is this game fair? Why? Make a prediction before you play. Play the game at least 5 times (i.e., tossing the chips until one of the players has 10 points) and record your results. Calculate the relative frequency of each player’s winning. On the basis of these trials, do you think the game is fair? Analyze the game by listing all possible outcomes or drawing a tree diagram. What is the theoretical chance of winning for each player? Game 2
Directions: Now add another red-red chip to the cup. In this game, if all three chips show red, Player A scores a point; otherwise, Player B scores a point.
| Player A gets 1 point. | | Player B gets 1 point. |
Is this game fair? Discuss with your group before you play. Play the game, and record and study the results. What is each player’s chance of winning? Suppose a red-red and two red-yellow chips are used. How does this change the outcomes? Is the game fair? Game 3
Directions: Suppose that a red-red chip is replaced by a second red-yellow chip. Again, if all three chips show red, Player A scores a point; otherwise, Player B scores a point.
How does replacing one of the red-red chips with a second red-yellow chip change the outcomes? Is Game 3 fair?
Game 4
Directions: Try this game with three chips—red-blue, red-yellow, and blue-yellow. Player A scores if all three chips are different colors; Player B scores a point if two chips match.
| Player A gets 1 point. | | Player B gets 1 point. |
Predict the fairness of this game. Discuss your reasons before playing. Play and record at least five games. Find the relative frequency of each player’s winning to decide if the game appears to be fair. How many outcomes are possible for this game? Make a tree diagram to help find the theoretical probability for each player. If this game is not fair, how would you change the scoring to make it fair? |