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

• ##### Report an Issue

To Replace or Not to Replace? That Is The Question

#### Activity Overview

In this activity, students explore situations that involve compound events with and without replacement. They use different ways to conceptualize theoretical probability.

#### 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 49 - 56 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
• Carry out four trials of a simulation of a compound event with replacement and a compound event without replacement
• Simulate 100 trials and pool the results of the entire class
• For each scenario carry out at least 2000 trials, to rule out the possibility of difference in relative frequency due to chance variation
• Understand that the probability of a same pick is greater in the compound event with replacement
• Observe how the relative frequency of the outcome changes if the sample size is increased while maintaining the same ratio in the compound event
• Summarize the combinations using a probability tree diagram for compound events or geometric area models
• #### 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