Carnival Probabilities

 

Project Overview

 

Purpose

 

In this project you will interpret, assess, and calculate probability and odds related to carnival games.

 

Process

 

At the end of the each lesson, under Project Connection, you will be required to complete the Module 2 Project. You can access the entire project from this page at any time.

 

Make sure to save all work from Project Connection in your course folder. You will submit your Module 2 Project to your teacher at the end of Module 2. Check with your teacher about how you should submit your project work before you begin the project.

 

Presentation

 

The most important part of your project presentation is clearly explaining and supporting your reasoning with relevant visuals and calculations. Make sure to show all your work.

 

Review the Module 2 Project Rubric to ensure you understand how you will be assessed on this project.

 

You can choose any format you prefer for the final presentation of this project. Some options include a written document, virtual or real poster, website, or video.

 

Project Steps

There are two parts to this project:

• Part 1 consists of completing questions to three games, which are in booths 1, 2, and 3.
• Part 2 consists of designing your own game, which is booth 4.

Part 1

 

Booth 1: Crazy Craps

 

In this game there are two different ways the player can win using a pair of fair dice. The player wins by throwing a sum of 2, 3, 4, 10, 11, or 12. The player also wins if doubles are rolled.

 

Let A represent winning by throwing a sum of 2, 3, 4, 10, 11, or 12. Let B represent winning by throwing doubles.

1. Create a graphic organizer to display all the possible outcomes.
2. Calculate P(A ∩ B).
3. Explain why P(A and B) ≠ 0.
4. The booth keeper has a sign at the booth that reads, “This is a fair game. Try your hand at it!” Use the theoretical probability that you calculated in question 2 to test the validity of the booth keeper’s sign by determining the odds of winning. Play the game at least three times.
5. Explain how the booth keeper calculated the 1 : 1 odds.
6. Increase your odds of winning by altering the rules of the game. Explain by stating the change in the rule and then showing mathematically that it increases the odds.

Save your responses in your course folder. Return to Lesson 2.

 

Booth 2: Raffle Fundraiser

 

The local hockey team is having a raffle to raise money. The team is selling 2500 tickets, and there will be two draws. The first draw is for the grand prize—a trip for two to an all-inclusive resort. The second draw is for the consolation prize—an HDTV. After each draw, the winning ticket is not returned to the raffle.

 

You buy 10 tickets for the raffle.

1. Calculate the probability of winning the HDTV.
2. What is the probability of winning at least one prize?
3. How could you change the rules of the raffle to make the events independent?
4. List at least two parameters you can change to give you better odds of winning the HDTV. Explain, by stating the change in the parameter and by showing mathematically, why this change of parameters increases the odds. Record you answer in a chart like the following.
   
   

   Description of Parameter Change	New Odds of Winning

Save your responses in your course folder.

 

Booth 3: Basketball Shot

 

The object of this game is to shoot a standard-size basketball through a standard-size basketball net. A ticket gives you two shots. If you sink one basket of the two, you win the small stuffed animal; and if you sink both baskets, you win the big stuffed animal.

 

Based on past experience, the probability of you scoring a basket on one shot is 35%.

1. Draw a tree diagram to display all the possible outcomes for your two shots.
2. What is the probability that you will win the small stuffed animal?
3. Explain how you can check to make sure that your tree diagram is correct.

Save your responses in your course folder. Did you make sure to answer all the questions thoughtfully and thoroughly? Did you show all your work for any mathematical computations?

 

 

 

Part 2

 

Booth 4: Design Your Own Carnival Game

 

The carnival manager feels the need to create an original game for the carnival. He has asked you to submit a proposal for this game. The game should be the type of game that you would play at a carnival or an amusement park, and it should appeal to other students who are in high school. You must be able to explain the probability of your game, so don’t make it too complicated. Don’t forget to list any prizes that can be won.

 

To help you organize your proposal to the carnival manager, follow the steps to give you the best chance for success.

 

Step 1: Include a description of all the necessary objects needed to play the game; for example, spinners, balls, or dice. Draw a picture of your game design, if necessary.

 

Step 2: You must create a set of step-by-step instructions that clearly explains your game. The instructions must be easy to follow so that anyone can pick them up, read them, and begin playing your game.

 

Step 3: Create a probability analysis. It should include the following:

• Describe whether the events in your game are mutually exclusive or non-mutually exclusive.
• Does your game involve two events? Explain whether the events are independent or dependent.
• Create one probability problem related to the game.
• Use a graphic organizer to display the possible outcomes.
• Provide a full solution to the probability problem.

Save your responses in your course folder. Return to Lesson 3.

 

Project Assessment

 

Your Module 2 Project will be evaluated by your teacher using the evaluation guidelines in the project rubric. Read the rubric carefully. Make sure you are aware of how you will be assessed. You can print or save a digital copy of the Module 2 Project Rubric as a guide to help you complete your project.

 

Don’t forget to submit your completed Module 2 Project to your teacher at the end of Module 2.