Phenomenological Probability

Robert Foote Disney Magnet School
4140 N. Marine Drive
Chicago IL 60613
(312) 534-5844


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.


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.

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