Download Step Right Up and Win a Prize

Step Right Up and Win a Prize
Introduction
What are my chances of winning? You probably ask yourself that question any time you play a game that offers a
prize for winning. You're about to embark on a gaming adventure. You'll investigate the mathematical probabilities of
winning various carnival games. You'll also research and design a game of your own. So, come on and take a chance!
Sharpen up that hand-eye-coordination and grab your probability tool kit. This adventure is a win-win situation!
The Task
Now that you have taken a chance and entered into the first part of your carnival adventure, please read over the
brief summaries of each challenge listed below. Don’t forget that the Resources section has some helpful Web sites
that you are advised to use, and the Guidance section has some useful tips to help get you started. Lastly, the Process
section has a detailed description of each game you are required to complete.
Game Challenge 1:
Using the given carnival games and their data, complete different probability calculations and make predictions based
on your calculated probabilities.
Game Challenge 2:
Second, research other carnival games and design a carnival game of your own. Then, prepare a report detailing why
your game would be good to include in a school carnival.
Game Challenge 3:
Third, create presentation of your findings that includes a scale model or scale drawing(s) of your game.
The Process
Below is a detailed description of each game challenge.
Game Challenge 1:
Listed below are descriptions of different carnival games and their rules. Use the information given to answer the
questions on the Games Worksheet.
Name
Characteristics
Alleycans
A ball is thrown at 10 different cans. Each can has a designated point value. There are 2 cans with a value
of 10, 2 cans with a value of 20, 2 cans with a value of 30, 2 cans have a value of 50, and 1 can with a
value of 100. Each time a ball is thrown it lands in one of the cans.
A dart is thrown at 100 different balloons. Each balloon has a designated point value of 0, 15, 25, 50, 75,
100. The following chart describes the number of balloons with each point value:
Balloon
Pop
Point
Value
Number of
Balloons
0
30
15
25
25
15
75
10
100
5
Ring Toss
There are 50 bottles. 25 of the bottles are blue. 15 of the bottles are red. 7 bottles are green, and 3
bottles are yellow. Multiple rings can be thrown on the same bottle.
Duck
Pond
There are 100 ducks in the pond. 15 ducks are marked with red dots, which can only be seen if the duck is
chosen from the pond. Once a duck is chosen, it is removed from the pond.
Games Worksheet
Name:__________________________________________ Date:__________
1. For the Duck Pond game, what is the probability that the first duck you choose will have a red dot and the
second one will not?
2. For the Ring Toss game, you are given three rings. What is the probability that you will throw one ring on a
red bottle, one ring on a blue bottle, and then one ring on a yellow bottle?
3. In the Alleycans game, what is the probability that with three different throws, the first two throws will be
worth 30 points each and the third throw will be worth 100 points?
4. In the Duck Pond game, if you are able to choose 3 ducks, what is the probability that you will choose at least
2 ducks with a red dot? at least 1 duck with a red dot? no ducks with a red dot?
5. Assuming that every time you throw a dart you will hit a balloon in the Balloon Pop game, what is the
probability that you will hit a balloon with a value of 0? or a value of 100? or a value of 0 or 100?
6. In the Balloon Pop game, if you throw three darts, what is the probability that you will hit 2 balloons with a
value of 15 and then one with a value of 25? (Hint: you cannot hit the same balloon twice.)
7. In the Alleycans game, what is the probability that with three different throws, none of the throws will be
worth 30 points?
8. Assuming that every time you throw a ring you will hit a bottle, what is the probability that given three
different rings you will hit the same green bottle twice and then 1 blue bottle in the Ring Toss game?
Game Challenge 2:
a.
Next, design your own carnival game. You can design a completely new game or redesign an existing game. Follow these
guidelines.
 The game must make a profit. Keep in mind the cost of the equipment and prizes you will need to make or buy for
your game.
 The rules of the game should be easily understood.
 The game should not take a long time to play.
b.
After designing a game that meets the above criteria find the theoretical probability of winning your game, if possible.
c.
Find a way to simulate your game at home or in the classroom. Play your simulation of the game several times, keeping a
record of your trials. Then calculate the experimental probability of winning your game.
d.
Write a report about your game that includes the following components:
 an organized record of your simulation trials;
 the probability of winning the game, both experimental and theoretical, if possible;
 how much money the game will cost to create and how much it will pay out if played several times;
 discuss what would be reasonable to charge for the game in order to make a reasonable profit; and
 explain why your game should be included in a school carnival and why you think people would want to play it.
Game Challenge 3:
Now it's time to put all of your findings together and create a presentation. Your presentation should include:


a scale model or scale drawing(s) of your game and
your report
Guidance
If you have questions about the different games, then you have come to the correct Web site. Below are some helpful hints for each
activity.
Game Challenge 1:
a.
b.
For a definition and to see some examples of how to calculate probabilities, refer to Lesson 9-1.
To see some examples and a definition of independent and dependent events, refer to Lesson 9-7.
Game Challenge 2:
For many games that are based solely on chance, calculating the theoretical probability of winning is relatively simple. For games
that are based on skill or a combination of skill and chance, calculating the theoretical probability of winning may be too difficult. If
you do not give the theoretical probability of winning your game, be sure to explain your reasoning for not doing so in your report.
Game Challenge 3:
a.
b.
c.
Be sure to provide the scale factor from the scale model or drawing(s) to the actual game.
Your model or drawings should be detailed enough so that anyone could use them to build your game.
Some of the presentations that you could create are:
 a Web page,
 a PowerPoint® presentation,
 a poster, or
 a video.
Resources
Below are some useful Web sites that you can use while completing this WebQuest. Remember, however, that you are not limited to
these sites.
www.schoolcarnivals.com
Google
Skeeball
Yahooligans
Conclusion
Now that you have picked apart different carnival games, what is the probability that you will participate in another game again?
Even in the small, amusing things in life you can find mathematics. Congratulations on successfully using your probability tool kit to
complete a difficult task.