11. Inferential Statistics

Lesson

Use probability to determine the fairness of a game of chance.

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

Two fair coins, Two six-sided number cubes, Paper and pen

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. |
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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,

How can you use probability to help you determine whether a decision is fair?

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