Investigation: Use probability to make fair decisions
Lesson
Objective
Use probability to determine the fairness of a game of chance.
Vocabulary
Define each of the terms below and be sure to use them when you discuss the activity below with your classmates.
- Sample space
- Probability
- Equally likely outcomes
Materials
Two fair coins, Two six-sided number cubes, Paper and pen
Procedure
Consider the three games below for the activity.
| Game A | Two players each toss one coin. If two heads turn up, the first player wins. If a head and a tail turn up, the second player wins. If two tails turn up, you play again. |
|---|---|
| Game B | Two players each roll a number cube. If the sum of the numbers is odd, the first player gets 1 point. If the sum is even, the second player gets 1 point. |
| Game C | Two players each roll a number cube. If the product of the numbers is odd, the first player gets 1 point. If the product is even, the second player gets 1 point. |
- For each game that is described above, list the sample space and determine the probability of the listed outcomes.
- They say that a game is a fair game if both players are equally likely to win. For each game above, determine whether its a fair game and then explain why or why not. Discuss your results with a classmate.
- If you determine that any of the games described is not a fair game, how could you change the rules to make it a fair game? Discuss your reasoning with a classmate.
- Work with a partner to design a simple game that appears to be fair but, due to a slight adjustment in the construction of the game—a change that a player may not notice—is actually unfair. Then, describe your game with other classmates,
Conclusion
How can you use probability to help you determine whether a decision is fair?