This assignment is based on a nationwide elementary school project on probability involving over 2000 students. We will perform the same task that these elementary school did during the project.
A brand of cereal has a free pen in each box. There are six different colors of pens, blue, green, yellow, orange, red, and purple. The question is, how many boxes, on average, does somebody have to buy in order to get at least one pen of each color? We assume that the cereal manufacturer purchased the same number of pens of each color for inclusion in their cereal, and so the probability of getting a certain color of pen in a single box is the same for each color.
To simulate buying enough boxes to get a pen of each color, we will roll a die, using the numbers as substitutes for the colors. Use 1 = blue, 2 = green, 3 = yellow, 4 = orange, 5 = red, 6 = purple. Roll the die, recording what color you get. Continue rolling until you have obtained each color.
Problem 1. Repeat the task 10 times, recording the tally of colors each time along with the number of rolls it takes to get each color.
Problem 2. Determine the class average for the number of rolls it takes to get each color. This is an approximation for the actual expected value for the task. For each color (e.g., die number) calculate the number of occurrences of the number divided by the total number of rolls. How close do you come to 1/6 for each color? Do you think it is reasonable to assume that each number on a die is equally likely to be rolled?
See http://lrs.ed.uiuc.edu/students/mcornell/cerealbox/index.html for information and data for the probable pen project.