Education Technology

To Replace or Not to Replace? That Is The Question

Published on 06/09/2008

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