Your school is planning a school carnival as a fundraiser. You and your group must create a game to run at the carnival. You need to prepare a report about your game to the carnival planning committee. Your report should include how to play the game, how to win, the materials needed, the possible outcomes, and the theoretical probability of each outcome. You should also play your game 50 times and record the experimental probabilities. Your report should also include a fundraising component that includes how much you would charge for each play of the game, what the prizes would be and how much they would cost, and how much money you would expect to raise after 100 plays of your game.

ACTIVITIES:

Activity

Due Date

Date Completed

Exploring Fair and Unfair Games Activity

Game Description and Rules

List of Possible Outcomes in a Table and a Tree Diagram

Theoretical Probabilities of each possible outcome listed as a decimal, fraction, and percent

Game was played 50 times and Results are Displayed in a Table

Experimental Probabilities are correctly written as a fraction, decimal and percent

Fundraising Report

Exploring Fair and Unfair Games

A game is fair if each player has the same chance of winning. In other words, a game is fair if the probabilities of each player winning are the same. Play these three games with a partner. Choose who will be Player A and who will be Player B

Game 1 - Place 1 red cube and 1 blue cube in a bag. Draw 1 cube from the bag without looking. If the cube is red, player A wins. If the cube is blue, player B wins.

Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.

Play the game 20 times and record your results in this table.

Tally

Total

Player A wins

Player B wins

Number of times played

20

Find the experimental probabilities for both players. P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Game 2 – Place 2 red cubes and 2 blue cubes in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.

Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.

Play the game 20 times and record your results in this table.

Tally

Total

Player A wins

Player B wins

Number of times played

20

Find the experimental probabilities for both players.

P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Game 3 – Place 3 red cubes and 1 blue cube in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.

Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.

Play the game 20 times and record your results in this table.

Tally

Total

Player A wins

Player B wins

Number of times played

20

Find the experimental probabilities for both players. P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Reflection Questions

1. Does a fair game always seem fair? Give examples why or why not.

2. If you and your partner played the same games tomorrow, will the experimental probabilities be the same that they are today? Explain why or why not.

3. If you and your partner played the same games tomorrow, will the theoretical probabilities be the same as they are today? Explain why or why not.

4. Fred and Julie played game 1. Fred won 7 times and Julie won 13 times. How can this happen if the game is fair?

5. Jamie and Jenny also played game 1. The first 3 cubes drawn were blue. Is the fourth cube more likely to be red or blue? Explain your answer.

Brainstorm ideas for fair and unfair games. Use coins, dice, spinners, cubes in a bag, or whatever you want.

Carnival GamesYour school is planning a school carnival as a fundraiser. You and your group must create a game to run at the carnival. You need to prepare a report about your game to the carnival planning committee. Your report should include how to play the game, how to win, the materials needed, the possible outcomes, and the theoretical probability of each outcome. You should also play your game 50 times and record the experimental probabilities. Your report should also include a fundraising component that includes how much you would charge for each play of the game, what the prizes would be and how much they would cost, and how much money you would expect to raise after 100 plays of your game.

ACTIVITIES:

ActivityDue DateDate CompletedExploring Fair and Unfair GamesA game is fair if each player has the same chance of winning. In other words, a game is fair if the probabilities of each player winning are the same.

Play these three games with a partner. Choose who will be Player A and who will be Player B

Game 1- Place 1 red cube and 1 blue cube in a bag. Draw 1 cube from the bag without looking. If the cube is red, player A wins. If the cube is blue, player B wins.Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.

P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Game 2– Place 2 red cubes and 2 blue cubes in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.

P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.Game 3– Place 3 red cubes and 1 blue cube in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.Find the experimental probabilities for both players. P(A wins) = _

P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

## Reflection Questions

1. Does a fair game always seem fair? Give examples why or why not.2. If you and your partner played the same games tomorrow, will the experimental probabilities be the same that they are today? Explain why or why not.

3. If you and your partner played the same games tomorrow, will the theoretical probabilities be the same as they are today? Explain why or why not.

4. Fred and Julie played game 1. Fred won 7 times and Julie won 13 times. How can this happen if the game is fair?

5. Jamie and Jenny also played game 1. The first 3 cubes drawn were blue. Is the fourth cube more likely to be red or blue? Explain your answer.

Brainstorm ideas for fair and unfair games. Use coins, dice, spinners, cubes in a bag, or whatever you want.

## RESOURCES:

§Introduction to Probability Lesson Online http://www.mathgoodies.com/lessons/vol6/intro_probability.html

· Explore probability concepts online with the following website http://nlvm.usu.edu/en/nav/category_g_3_t_5.html

## ASSESSMENT RUBRIC: You will be graded according to the following rubric.

NoviceApprenticePractitionerExpertGame DescriptionPractitionerplus explains whether or not the game is fair and your reasons for choosing the gameTheoretical Probabilitiesorshown in a tree diagramandshown in tree diagramandshown in a tree diagramPractitionerplus includes the odds of each outcomeExperimentalProbabilitiesora percentandpercentPractitionerplus game results are shown in graphsFundraising ReportPractitionerplus compares the game to a common carnival gameMathematical ComputationsMathematical Content/Mechanical Criteria