Phenomenological Probability
                              
Robert Foote                   Disney Magnet School
4022 N. Monticello             4140 N. Marine Drive
Chicago IL 60618               Chicago IL 60613
(312) 604-8825                 (312) 534-5844

Objective:

Students will find the difference between theoretical and experimental 
probability in three different experiments.  This mini-teach is designed for 
junior high students. 

Materials Needed:

* A pair of dice for each student
* Ten or more colored marbles and a spinner (or bag)
* A standard deck of 52 cards.

Strategy:


Set up three stations with the materials mentioned above at each station.  Give 
students about twenty minutes for each activity.  Blow a whistle or clap between 
each activity and then have groups switch activities.  The following is a 
description of each activity: 

1. Rolling Two Dice:  Have each student roll two dice 20 times and record each 
sum.  When the experiment is completed, have each student come up with a group
probability by combining the individual experiments.  Experimental probability 
is the number of times a sum is rolled divided by the number of rolls (20).

2.  Marbles in a  Spinner:  For this experiment, I used a spinner that allowed 
one marble to land in a space on the spinner.  You may do the same experiment 
without the spinner using a bag and having students pick a marble out of the bag 
20 times.  Make sure you have different color marbles of different amounts  so 
you have different probabilities for each color.  Compute experimental 
probability by keeping track of how many of each color are picked or land in the 
spinner.  Experimental probability here is the number of the color picked 
divided by the total marbles picked. 

3.  Card Trick: Have each student in the group pick a card from the deck, 
shuffle the cards and pick another card five times.  The student will pick a 
total of five cards.  To determine experimental probability, find the desired 
outcome such as number of face cards, over the total numbers of cards drawn.

After all the experiments are performed and experimental probabilities are 
found, compare them to the theoretical probabilities of each experiment.  You 
may determine how close the two are as fractions, decimals, and percents.  

Performance Assessment:

An easy performance assessment of this lesson would be to use the same 
experiments with slight modifications such as adding one die,more marbles,or 
changing the card events.  You can thus assess student understanding of 
probability using the experiments and have them compute them on their own by 
writing up their own calculations from the experiment and comparing them to the 
theoretical probability.