# Learn By Doing – Empirical Probability #1

## Purpose

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.

## Video Illustration

## Part (A)

- Be sure that the
**Animate**option is checked. - Let
**n****= 1**and press the**Flip**button 3 times. - 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.** - 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)

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

## Hint

## Part (C)

- 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.