The Probability Simulation application on the TI-84 Plus calculator can simulate rolling from one to three dice at a time. It can even roll weighted dice. When rolling only one die at a time, the application keeps track of the number of times each number on the die lands up as the die is repeatedly rolled.

When rolling more than one die at a time, the application keeps track of the sum of the numbers on the dice.

The data from the repeatedly rolling the dice can be displayed in a histogram or in a table. The application even gives you the option of saving your data so you can, if you choose, statistically analyze it at a later time.

How to roll dice in Probability Simulation

To roll dice, follow these steps:

1. Start the Probability Simulation application and press [2] to select the Roll Dice option in the Main menu.

You see the Roll Dice Home screen, as illustrated in the first picture.

To use the Roll Dice simulator after using another simulator, repeatedly press [Y=] until you see the Main menu, and then press [2] to select the Roll Coin simulator.

2. Press [ZOOM] to display the Settings editor. Change the settings in Settings editor as appropriate.

You see a screen similar to the Toss Coins simulator’s Settings editor.

The Dice option lets you tell the application to roll 1, 2, or 3 dice each time it rolls dice. The Sides option lets you roll normal six-sided dice or exotic dice having 8, 10, 12, or 20 sides. If you are rolling more than one die, all your dice must have the same number of sides.

To enter a number in Trial Set, use the arrow keys to place the cursor on the existing number, use the keypad to enter a new positive integer, and then press [ENTER]. To select other options, use the arrow keys to place the cursor on the option and press [ENTER] to select the option.

Don’t forget the Update option. The down arrow in the lower-right corner of the screen indicates that you should repeatedly press

to reach this option.

3. Press [WINDOW] to display the Advanced Settings editor. Enter the weights for your dice.

The screen you see lists the sides of a die in the first column, its weight in the second column, and the probability of that side landing face up in the third column. If you are rolling more than one die, the application requires that all of the dice be weighted in the same way.

4. Press [GRAPH] to say OK to the weights in the Advanced Settings editor. Press [GRAPH] again to say OK to the settings in the Settings editor.

You see the Roll Dice Home screen. If you are rolling more than one die, you see a jumble of numbers on the screen.

5. Press [WINDOW] to roll dice.

You see a screen similar to the second picture. If in Step 2 you set Trial Set to 1, then only one bar appears in the histogram. If you set Trial Set to a number greater than one, then the command line at the bottom of the screen is the same command line as in the first picture.

6. Continue rolling dice.

If in Step 2 you set Trial Set to a number greater than one, press [WINDOW] to roll more dice.

If Trial Set is 1, then after rolling the first set of dice, you see a screen similar to the second picture. Press [WINDOW] to roll one more set of dice, [ZOOM] to roll ten more sets of dice, or [TRACE] to roll 50 more sets of dice.

How to read the Roll Dice graph and table

The cumulative data from rolling dice is stored in both a histogram and a table. The histogram, by default, is displayed on the screen without any values on the y-axis. Here are some specifics about the Roll Dice histogram and table:

• Roll Dice histogram: If you are rolling only one die, the histogram displays the cumulative outcomes of the side of the die that landed face-up. If you are rolling more than one die, the histogram displays cumulative outcomes of the sum of the face-up sides of the dice.

For example, if you are rolling three dice, the possible outcomes (sums of face-up sides) are the integers 3 through 15. These numbers appear below the histogram with the two-digit numbers displayed in a column. The right arrow indicates that there are too many bars in the histogram to display on the screen. Repeatedly press

to see these bars.

• Roll Dice table: The number of the roll appears in the first column of the table. The middle columns contain the outcome (number that landed face-up) for each die, and the last column contains sum of the outcomes for the dice in that roll. If you are rolling only one die, the middle and last column will, of course, be the same.