Assignment: Probability Project Extra Credit

Geometry Applications of Probability
2022-07-05T20:04:45Z

Due: Jul 22, 2022 by 11:59pm

Probability Project Directions

Design a carnival game for inclusion in the upcoming Georgia State Fair. Be sure to be creative and realistic. Do not make up a game that cannot be made and played. Think – State Fair…

1. Create a game and name it – be sure to list all group members under the game name

1. Video you playing your game – your game should be able to be played in class. Bring in everything you need to play it.

2. Include a report with your model that details the following items. Place A and C on one page and then each letter on a different page (piece of paper). Turn your project in with A first, then C, then D, etc.

3. Rules of the game

1. Clearly states the rules, which are easy to understand, and cover all possibilities.

2. Your game must include at least two actions or rounds.

3. Make sure your game is playable by the rules you set.

4. Set the cost, the goal is to make money on your game but it has to entice the players!

4. Experimental

1. Play your game all the way through at least 20 times

2. Use those results to find your probability for every outcome.

3. Show the recording of all the results and how you calculated probability.

5. Theoretical

1. Create a tree diagram showing the probabilities for all events and outcomes.

2. Determine the probability of each event in playing the game.

3. For skill games (ask if you don’t know) complete the following.

4. Try each needed skill 100+ times (show your chart of results)

1. Use the results for the probability of each skill

2. Create a summary chart and show how you calculated probability

3. This is two pages if skill based: Tree Diagram and Summary Chart

4. You may need to not count misses (retry) to simplify your probability.

6. Prizes and how to earn the prizes

1. Lists prizes with cost and how they are won in a chart (Prize, cost, won).

7. Expected payoff

1. Gives YOUR correct expected payoff (make money) and how it was calculated.

2. Use your experimental probability to find your expected payout.

3. Give the expected payoff from YOUR perspective for playing 1 game.

4. Show all your work!

8. Expenses

1. Correctly computes and calculates expense total for the game.

2. Research and record the cost of anything (prizes, materials) needed for the game.

3. Be sure to figure out expected number of prizes, materials you will need for 500 games.

4. Use the experimental probability to find your expected number of prizes.

9. Profit

1. Correctly computes the profit (income – expenses) from your perspective.

2. Calculate your expected profit if 500 people play your game at the carnival.

10. Why the game should be selected for the carnival

1. Clearly addresses WHY people would want to play the game and WHY it should be in the carnival. Checked for grammar, spelling, punctuation and must be 5 sentences.

Module Objectives

1.1 Identify the sample space total of an event.

1.2 Determine the theoretical and experimental probability of an event.

1.3 Recall and use Complement formula.

1.4 Determine geometric probabilities.

1.5 Determine probability of compound events using the Multiplication Rule for Independent Events.

1.7 Determine compound probability of multiple events.

2.1 Determine compound probability of multiple events.

2.6 Identify and differentiate between a union and intersection of compound events.

2.7 Determine the probability of compound events using the Addition Rule.

2.8 Explain why conditional probability changes when the order of events changes.

Probability Project Directions

Design a carnival game for inclusion in the upcoming Georgia State Fair. Be sure to be creative and realistic. Do not make up a game that cannot be made and played. Think – State Fair…

1. Create a game and name it – be sure to list all group members under the game name

1. Video you playing your game – your game should be able to be played in class. Bring in everything you need to play it.

2. Include a report with your model that details the following items. Place A and C on one page and then each letter on a different page (piece of paper). Turn your project in with A first, then C, then D, etc.

3. Rules of the game

1. Clearly states the rules, which are easy to understand, and cover all possibilities.

2. Your game must include at least two actions or rounds.

3. Make sure your game is playable by the rules you set.

4. Set the cost, the goal is to make money on your game but it has to entice the players!

4. Experimental

1. Play your game all the way through at least 20 times

2. Use those results to find your probability for every outcome.

3. Show the recording of all the results and how you calculated probability.

5. Theoretical

1. Create a tree diagram showing the probabilities for all events and outcomes.

2. Determine the probability of each event in playing the game.

3. For skill games (ask if you don’t know) complete the following.

4. Try each needed skill 100+ times (show your chart of results)

1. Use the results for the probability of each skill

2. Create a summary chart and show how you calculated probability

3. This is two pages if skill based: Tree Diagram and Summary Chart

4. You may need to not count misses (retry) to simplify your probability.

6. Prizes and how to earn the prizes

1. Lists prizes with cost and how they are won in a chart (Prize, cost, won).

7. Expected payoff

1. Gives YOUR correct expected payoff (make money) and how it was calculated.

2. Use your experimental probability to find your expected payout.

3. Give the expected payoff from YOUR perspective for playing 1 game.

4. Show all your work!

8. Expenses

1. Correctly computes and calculates expense total for the game.

2. Research and record the cost of anything (prizes, materials) needed for the game.

3. Be sure to figure out expected number of prizes, materials you will need for 500 games.

4. Use the experimental probability to find your expected number of prizes.

9. Profit

1. Correctly computes the profit (income – expenses) from your perspective.

2. Calculate your expected profit if 500 people play your game at the carnival.

10. Why the game should be selected for the carnival

1. Clearly addresses WHY people would want to play the game and WHY it should be in the carnival. Checked for grammar, spelling, punctuation and must be 5 sentences.

Module Objectives

1.1 Identify the sample space total of an event.

1.2 Determine the theoretical and experimental probability of an event.

1.3 Recall and use Complement formula.

1.4 Determine geometric probabilities.

1.5 Determine probability of compound events using the Multiplication Rule for Independent Events.

1.7 Determine compound probability of multiple events.

2.1 Determine compound probability of multiple events.

2.6 Identify and differentiate between a union and intersection of compound events.

2.7 Determine the probability of compound events using the Addition Rule.

2.8 Explain why conditional probability changes when the order of events changes.