Now that you have modelled the problem with a die and seen the
theoretical expected value,
try this online demonstration of the problem.
6/1 + 6/2 + 6/3 + 6/4 + 6/5 + 6/6 = 14.7
"Similarly, it can be shown that for an eight sided die, the theoretical number (expected value) of rolls needed to get all eight sides is
8/1 + 8/2 + 8/3 + 8/4 + 8/5 + 8/6 + 8/7 + 8/8 = 21.7
Use this pattern to find the expected number of rolls of a 12-sided die to get all 12 sides. Then use a 12-sided die, a spinner, or some other appropriate model and conduct 50 trials. Compare your estimated number of rolls of the die with the theoretical value given by this formula"*
Now that you have modelled the problem with a die and seen the
theoretical expected value,
try this online demonstration of the problem.
For a full analytic explanation of the mathematics behind this problem, see "The Cereal Box Problem" by Jay Wilkins (PDF file).
This is the end of the lesson. Please send feedback by clicking on the mail icon and filling out a message.
*From Using Statistics, by Travers, Stout, Swift, and Sextro. Addison-Wesley Publishing Company. 1985.
Last edited May 15, 1996