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4-7

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## Probability and Fairness

Students are introduced to the concept of probability through problems concerning fairness in games and the odds of winning or losing a game of chance.

### Overview

In this Cyberchase activity, students are introduced to concepts of fairness in games based on the probability, or odds, of winning and losing a game of chance. This activity is motivated by a Cyberchase video segment in which the CyberSquad plays a fair game of chance called the Squares Game and one game created by Hacker.

4-7

1 hour

### Media Resources

The Squares Game QuickTime Video
Hacker's Four-Zergen Game QuickTime Video

### Part I: Learning Activity

1. Discuss the idea of a coin having a 50% probability of landing with its head up ("heads") and a 50% probability of landing with its head down ("tails"), if the coin is "fair."

2. Tell the students that they will watch a video segment in which the CyberSquad has to determine whether the "Squares" game is fair.

3. Show the The Squares Game QuickTime Video, and pause it after Lucky wins.

4. Discuss with the students whether they think the game is "fair."

5. Show the students the rest of the video segment in which the CyberSquad defines "fair" as an "equal chance of winning"and analyze the chances as 3 out of 9 or 1 out of 3.

6. Distribute the Four Zergens in a Hat handout .

7. Introduce students to the "4 Zergens in a Hat" game using the handout.

8. Tell the students that they will next watch a video in which theCyberSquad analyzes the game. Ask them to see if their analysis agrees with the CyberSquad's in the video segment.

9. Show the Hacker's Four-Zergen Game QuickTime Video .

10. Discuss different ideas. End by reinforcing the idea that the odds of winning are 1 out of 6 and the odds of losing are 5 out of 6.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to assess the fairness of a version of the Squares Game in which there is a 4 x 4 board, and different numbers of black and white squares.

Assessment: Level B (above proficiency): Students are asked to figure out the odds of winning aversion of Hacker's game that uses 6 zergens instead of 4.

## Educational Standards

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