The study of probability and statistics is becoming increasingly emphasized in mathematical texts and curriculum. Probability is usually introduced in elementary or middle schools by spinning wheels or rolling dice. These types of hands-on activities are necessary for developing a strong conceptual foundation. With computers becoming increasingly common, another valuable tool for experimental probability is the computer spreadsheet.

Any computer spreadsheet can be set up to simulate random events. This particular activity will explain how to use Microsoft Excel (1995) to simulate the rolling of two dice. The question we are trying to answer is "What is the most common sum that will occur when two dice are rolled?" We will set up a spreadsheet to simulate 20 simultaneous rolls of the dice, tabulate the results, and output the results in numerical and graphical form. Spreadsheets such as this are actually quite simple to create and can be saved on disk and used again as needed.

Begin by setting up columns labeled as in Figure 1. The underlying formulas can be seen in Figure 2. The randbetween function in Excel has two parameters, randbetween(lowerbound, upperbound). For example, randbetween(1,6) generates a random integer in the range of 1 through 6. Figure 3 uses the rand function which is common to most mathematical packages. In Excel, the calculation mode should be set to Manual. This is accomplished by going to the Tools menu, then the Options... menu item, and finally the Calculation tab on the dialog window that will come onto the screen. By choosing Manual calculation mode, the user can control when the spreadsheet "throws" the dice. This is done in Excel by hitting the F9 key on Macintosh and PC computers, or Command+= on the Macintosh. When you want another twenty rolls of the dice, you simply do another manual calculation. The chart will make the corresponding changes (See Figure 4).

Of course you are not limited to only 20 rolls of the dice. As we increase the number of rolls our experimental outcome should approach the predicted theoretical outcome. Figure 5 shows the experimental outcome, and Figure 6 is the theoretical outcome after only 5000 rolls with the dice. These same types of experiments can be done through programming on a computer or graphing calculator. But I believe the spreadsheet method is so straightforward for both teachers and students, with both the numerical calculations and graphical results on a large screen. Attention is focused on the mathematics of experimental probability, rather than the programming of setting up the problem.

Bibliography