Project C07 - Simulations with the Research Randomizer

In many situations, theoretical probabilities and expected values can be extremely difficult to determine. Yet, in these situations, it may also be impractical or inconvenient to experimently determine them. Consider the following example taken from A Problem Solving Approach to Mathematics for Elementary School Teachers, 6th Edition; Billstein, Libeskind, & Lott (page 446, #16):

Montana duck hunters are all perfect shots. Ten Montana duck hunters are in a duck blind when 10 ducks fly over. All 10 hunters pick a duck at random to shoot at, and all ten hunters fire at the same time. How many ducks could be expected to escape, on average, if this experiment were repeated a large number of times?

To determine the expected value theoretically would a be difficult task for a beginning probability student. On the other hand, even if Montana duck hunters were perfect shots, it would impractical and illegal to repeat the experiment a large number of times. In a case such as this, simulations provide a way of estimating probabilities and expected values.

In this project, you will use an on-line tool called the Research Randomizer (http://www.randomizer.org/index.htm) to simulate several experiments. As you work you should keep the following objectives in mind.

• Objective 1: Enjoy and be challenged by mathematics.
• Objective 2: Practice designing and carrying out simulations, and interpreting the results.
• Objective 3: Read and write mathematics effectively.
• Objective 4: Gain experience in using the internet as a research tool.

The following rules and guidelines apply to this project:

• You may collaborate with your classmates, but each student must turn in her or his individual (and unique) solution set.
• Show all work on separate sheets of notebook paper. Be neat and orderly, and clearly indicate to which page your work corresponds. As a general rule of thumb: If you think it, show it!
• Be sure that all explanations are given in complete, grammatically correct sentences. Explanations must appear in the boxes provided.
• Print the appropriate pages upon completion. You must submit these pages along with your work. Be sure that your name appears on the first page.
• Follow the link below to begin with Page 1 of the project.

Page 1 | Page 2 | Page 3 | Page 4 | Page 5 | Page 6

The Research Randomizer is an on-line tool. You must work this project on-line.

Steve Kifowit Prairie State College Chicago Heights, IL 60411