W. Gary Martin home page > CTSE 7970 > Write-up #2
CTSE 7970, Summer 2001, Write-up #2 – Dicey Differences
For this exercise, assume only the basic definitions of probability. Use Excel to explore the phenomenon, both experimentally and theoretically. Make judicious use of graphs to help explain.
1. Roll two dice and find the difference of their values, subtracting the larger value from the smaller.
a. Set up a spreadsheet to simulate the differences generated by 1000 rolls of two dice. (HINT: You may want to use the “ABS” function.) Then compute the frequencies of the differences. What difference is most likely? Least likely? What is the likelihood of getting other differences?
b. Set up a spreadsheet showing all the possible events that could occur. That is, set up a table with the possible rolls of one die in column A, and the possible rolls of the second die in row 1. Then calculate the differences as the entries in a 6x6 table. Finally, compute the frequencies, using the range of values (such as A2:G7) as the first argument for the function. Discuss the likelihood of getting various differences.
c. Compare your answers to parts (a) and (b). How are they the same or different? Why?
2. Your teacher bought some fancy dice with other numbers of (congruent) faces.
a. Repeat #1 for the following kinds of dice:
- Decahedron
- Octahedron
- Dodecahedron
b. Can you find a general pattern for the probabilities of various differences when using dice with n faces? Explain why your pattern works.
NOTE: To enhance this exploration, you will probably use a named value, say “faces”.
- This will work well in exploring 1(a).
- However, exploring 1(b) will be more difficult, since the dimensions of the array of values to be counted up in the FREQUENCY function depend on the number of faces. Here is a hint:
- Set up a large table of values, say 20 by 20. Then use the OFFSET function to select a subset of that table.
- Here is the format: OFFSET(reference of the first cell in your table, first row, first column, number of rows, number of columns). Depending on where you set up your table, the first cell will probably be B2. Since you want to begin counting at the upper left corner, the first row and column will both be 1. The number of rows and columns correspond to the number of faces.
- Your OFFSET array will be the first argument for the FREQUENCY function.
3. By mistake, Bobbie picked up two different kinds of dice, one a dodecahedron and the other a tetrahedron.
a. How does this affect the probabilities?
b. Generalize your findings for any two kinds of dice. (HINT: Use two different named values!)