Author:
Christopher Danielson

To demonstrate the use of computer software to perform simple probability situations.

There are many cases of probability questions that are stated quite simply, but whose theoretical probabilities are really hard to figure out. In these cases, we might be interested in performing an electronic simulation to calculate experimental probabilities. This is a kind of simulation (or Monte Carlo simulation) and spreadsheets make it easy to do this quickly.

This packet demonstrates the specifics of this process for a simple example-rolling two dice and calculating the sum-using three software packages: Microsoft Excel, Apple Numbers and GeoGebra.

Tutorial

There are plenty of questions in the study of probability where calculating an exact theoretical probability is very challenging-even in relatively simple situations. In these cases, it is often desirable (and sometimes essential) to begin with experimental probabilities.

When we are performing experiments to gather data for experimental probabilities, the time or monetary investment might be large, so instead we can use computer software to gather the data for us.

As a simplistic example, if we want to estimate the probability of rolling a sum of 7 when rolling two dice, we might want to roll 50 times. We roll, put down the dice, pick up our pencil to write down the results, roll again, etc. This can take a while, and then if we want to repeat the experiment, we have to do it all over again.

An electronic simulation will go much more quickly, will keep track of our data along the way and can be instantly repeated as many times as we like.

The remainder of this packet consists of links to three tutorials for doing this. The first uses Microsoft *Excel*, the second uses Apple's *Numbers* and the third uses *GeoGebra*, which is freeware available at www.geogebra.org. They all follow the same basic idea; you should watch whichever video matches the spreadsheet you will be using. If you have some other spreadsheet (e.g. Google Docs), watch any of these and your spreadsheet will work pretty much the same way-you'll have to modify the specific commands but you can figure it out.