Fun with Probability! The Probable Pen in the Cereal Box 
Student Worksheet    Name __________________

1. Predict the number of pens you will get for each color, 
and the total number of pens.
 
2. Using each side of a die to represent one colored pen, 
tabulate the number of rolls it takes until you have at
least one of each color.
 
3. Count the total for each color and record the total 
number of pens you got.
 
4. Predict the total number of each color for your whole 
class, and the total number of pens for your whole 
class.
 
                   Die1  Die2  Die3  Die4  Die5 Die6
                   Blue   Grn   Yel   Org  Red   Pur  Tot
1. Prediction
2. Tally
3. Actual Totals
4. Prediction of
   Class Totals
5. Actual
   Class Totals
                                                 
Questions 
1. How many boxes of cereal did you have to purchase to 
get one pen of each color? ______ (Remember, you had 
to buy one box of cereal to get each pen).
 
2. How many boxes did you predict? ______ Was it more or 
less? ________
 
3. Why do you think your prediction is different from 
the actual? _______________________________________________

4. How many boxes did your entire class buy? ________
 
5. What was the average or mean number of boxes per 
student? The average can be calculated by dividing 
the total number of boxes (#4) by the total number of 
students. __________
 
6. The expected value is the number of boxes we would 
expect to buy on average if we repeated this 
experiment over and over. For this problem, the 
expected value is _____.
 
7. Was your class's average (#5) more or less than the 
expected value? (#6) ______
 
8. Why do you think this is the case? ____________
 
Copyright (c) University of Illinois, 1996