# Activities

• • • ##### Subject Area

• Math: Statistics: Probability and Random Variables

• ##### Author 9-12

60 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 3 from the EXPLORATIONS Book:
Exploring Mathematics with the Probability Simulation Application.

## Law of Large Numbers: Adding It Up

#### Activity Overview

In this activity, students examine the relationship between relative frequency and theoretical probability to understand the Law of Large Numbers. They will explore the concept of independent events. They will also discern the difference between relative and cumulative frequencies.

#### 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 35 - 46 from the attached PDF file for your class

#### During the Activity

Distribute the pages to your class.

• Start the Probability Simulation application
• Simulate the tossing of a coin 400 times
• Create a bar graph for the total number of tosses and frequency of heads and tails
• Calculate the cumulative frequency for the coin landing heads up for each coin toss
• Create a line graph of the relative frequency for the coin landing heads up for each coin toss
• Graphically view the first 25 tosses of the coin versus this relative frequency
• Observe the plot for the first 100 tosses
• Compare the tables and graphs for relative frequency of the first and last 25 tosses
• Understand that as the number of trials increases, the difference between the relative frequency of success and the probability of success approaches zero; while the difference between cumulative frequency of success and expected number of successes tends to grow
• #### 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