# 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. 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. 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.
1. For each game that is described above, list the sample space and determine the probability of the listed outcomes.
2. 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.
3.  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.
4. 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?

### Outcomes

#### S-MD.6

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).