Education Technology

# Activities

• ##### Subject Area

• Math: Statistics: Probability and Random Variables

9-12

90 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book:
Exploring Mathematics with the Probability Simulation Application.

The following accessory is required for this activity:
• ViewScreen Panel™ or TI-Presenter™ video adapter

## Law of Large Numbers: A Weighty Decision

#### Activity Overview

In this activity, students will explore the Law of Large Numbers. By examining unfair models, they will expand their understanding of probability. They predict the weighting of an unfair model by analyzing experimental data and distributions. They will also formulate and test a hypothesis on the fairness of models.

#### Before the Activity

Install the Probability Simulation Application on the calculator using one of these two methods:

• TI Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™ "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 17 - 28 from the attached PDF file for your class

#### During the Activity

Distribute the pages to your class.

Follow the Activity procedures:

• Start the Probability Simulation application
• Weight one section of a spinner more than others in the Spin Spinner Simulation
• Observe the changed probabilities for each section
• Change the weight of other sections and observe the change in the probabilities
• Look for patterns and predict the probability of a change in weight
• Calculate the theoretical probability for a biased model
• Change the weights for each side of a die in the Roll Dice simulator
• Graph the results of 60 trials for a weighted die and discern the difference between normal experimental variance and results of a biased experiment
• At the end of 240 trials, observe that the results more consistently resemble the shape of the theoretical distribution
• Examine data and determine if a die is weighted and determine the weights assigned to each side
• #### After the Activity

Students will complete the Student Worksheet and answer questions.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary