Education Technology

Demonstrating Probability, Simulations, and Probability Distributions

Published on 06/09/2008

Activity Overview

This activity demonstrates the probability of an event happening with the simulation of a coin toss. Students will learn how probabilities can be computed. They will simulate distributions to check the reasonableness of the results. They also explore various probability distributions.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 51 - 71 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

    The Law of Large Numbers:

  • Simulate the tossing of coins (150 trials)
  • Observe that the proportion of heads approximates to 0.5 after 150 trials

  • Factorials, Permutations, and Combinations:
  • Use the calculator to compute factorials, permutations, and combinations

  • Distributions:
  • Obtain a selection set and determine the probability density functions
  • Compute approximate probabilities for the event
  • Set up a probability histogram

  • Distribution of Sample Proportions:
  • Set the binomial simulator to represent one pick at a time with a 0.67 chance of success
  • Generate a set of zeros and ones as a simulation
  • Calculate the proportion of success
  • Set up a histogram and highlight the class which contains the value of 0.67
  • Observe that the distribution is skewed
  • Develop a frequency table and determine the mean and standard deviation
  • Understand that as the sample size increases, the distribution gets more normal

  • Central Limit Theorem:
  • Simulate the distribution of sample means from a continuous uniform distribution with all possible values between 1 and 10
  • Generate 100 random values between 1 and 10
  • Compare the theoretical and experimental means and standard deviations for various sample sizes
  • Construct a histogram

  • Normal Probability Plots:
  • Graph a normal probability scatter plot for the data
  • Check whether the distribution is symmetric or skewed and assess the normality
  • After the Activity

    Review student results:

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