In this activity, you will use a die and a tally sheet to model the cereal box problem. One roll will represent a trip to the supermarket. Each number on the die will represent one of the prizes. You should do at least 30 trials. One trial is complete when you have all six prizes.
Below is a table that illustrates 5 trials. The first trial turned up prize #1 three times, and prize #3 five times. Can you tell which was the last prize for each trial? How?
Now make your own table like this one. Instead of numbers, you will probably have tally marks in your table.
| Trial | Prize #1 | Prize #2 | Prize #3 | Prize #4 | Prize #5 | Prize #6 | Total Number of Rolls |
|---|---|---|---|---|---|---|---|
| Trial #1 | 3 | 1 | 5 | 2 | 2 | 3 | 16 |
| Trial #2 | 2 | 2 | 2 | 2 | 2 | 1 | 11 |
| Trial #3 | 2 | 3 | 1 | 2 | 2 | 2 | 12 |
| Trial #4 | 1 | 4 | 2 | 4 | 3 | 4 | 18 |
| Trial #5 | 2 | 2 | 1 | 3 | 3 | 9 | 20 |
An empty table is available for print out.
After you have have completed your table, find the average of all the trials done by your class. (For example, in the table above, the average is 77/5 = 15.4) This is your experimental expected value. Now check and see how close this is to the theoretical value.
Interested in the mathematics of the cereal box problem?
Check out the following article by Jesse "Jay" Wilkins, Wilkins, J. L. M. (1999).
The cereal box problem revisited
.
School Science and Mathematics, 99(3), 117-123.
Click on the title to download the article in Adobe Acrobat format.
Special thanks to School Science and Mathematics, for allowing us to distrubute the article in this manner.