Education Technology

TAS: Sampling With and Without Replacement

by Frank Moya


  • To explore how the results obtained from random sampling vary from sample to sample.
  • To estimate probabilities of an events from dotplots and histograms generated from the results of simulations.
  • To compare probabilities for selections made with and without replacement.
  • To use tree diagrams or other suitable approaches to find theoretical probabilities for selections made with and without replacement, and to compare the theoretical results with the estimated probabilities obtained by simulation.


  • Random Sample
  • Dot-plot and Histogram
  • With and Without Replacement
  • Probability Distribution

About the Lesson

Students simulate drawing random samples of 3 marbles, selected with and without replacement, from an urn containing 10 marbles. Comparisons are made between the results obtained for these selection methods. The effect of increasing the number of trials in the simulations is explored. Finally, comparisons are made between the simulation results and the theoretical probability distributions of the random variables associated with these random processes.