Learn By Doing – Empirical Probability #1


The purpose of this activity is to experiment with an applet that simulates flipping a fair coin, and to see if the P(H) = 0.5.

The link below will launch the applet in a new window.  Note that the green horizontal line shows P(H) = 0.5.

Interactive Applet: Coin Flips  

Video Illustration

Part (A)

  1. Be sure that the Animate option is checked.
  2. Let n = 1 and press the Flip button 3 times.
  3. Notice that for each flip, you will see either head or tail appear for the Flips and the cumulative proportion of heads will change. Also, the graph will display the P(H).So, if your first flip is a tail then P(H) = 0, a dot appears at 0, and Cumulative Proportion of “Heads” = 0/1 = 0. However, if the first flip is a head then P(H) = 1, a dot appears at 1, and Cumulative Proportion of “Heads” = 1/1 = 1. 
  4. When you press the Flip button the second time, the result is recorded as a head or a tail, a new P(H) is calculated based upon the number of heads you got out of two flips, the cumulative proportion of “Heads” is adjusted to reflect the flip, and a dot for that value is plotted.

Part (B)

  1. After you have pressed the Flip button 3 times, press the Reset button so that everything is cleared and you can start over.
  2. This time let n = 10. Again press the Flip button 3 times, without resetting.



Part (C)

  1. Last, after resetting, let n = 100 and press the Flip button. To speed up the next 100 flips, uncheck Animate. Press the Flip button a few more times, so that you have a total of at least 1,000 flips.


This document is linked from Introduction to Probability.