Prob Sim App

The Prob Sim app performs the six types of simulations described below.

Coin Toss

Dice Roll

Spinner

Marble Grab

Card Draw

Random Numbers (Random Integers)

Operation Flow

Step 1: Select a simulation type (Probability tab).

h > Prob Sim

This displays a menu for selecting a simulation type.

Highlight the type of simulation you want to run and then press > (or O).

This displays the Setup tab, which shows the settings for the type of simulation you chose.

Step 2: Specify the number of simulation trials and configure other settings (Setup tab).

Specify the number of simulation trials.

Highlight [‎# of Trials] and then press O.

In the dialog box that appears, input an integer between 1 and 999 and then press O.

Configure other settings.

Setting Items Specific to Particular Simulation Types

Type	Item	Description	Setting^*1
Coin Toss	Coins	Specifies the number of coins.	1, 2, 3
Dice Roll	Dice	Specifies the number of dice.	1, 2, 3
Dice Roll	Die Sides	Specifies the number of faces for each die.	4, 6, 8, 12, 20
Spinner	Sections	Specifies the number of divisions on the spinner.	2, 3, 4 to 8
Marble Grab	Marble Types	Specifies the types of marbles. Selecting 2 for this setting will specify A, B for the marble types, while selecting 5 will specify A, B, C, D, E.	2, 3, 4, 5
Marble Grab	Replacement	Specifies whether a drawn marble is replaced (On) or not (Off) after being drawn. “” is displayed in the upper left corner of the result screen when On is selected for replacement.	On, Off
Card Draw	Decks	Specifies the number of card decks.	1, 2, 3
	Deck Size	Specifies the number of cards in a deck.	32, 52
	Replacement	Specifies whether a drawn card is replaced (On) or not (Off) after being drawn. “” is displayed in the upper left corner of the result screen when On is selected for replacement.	On, Off
Random Numbers	‎# of RanNums	Specifies the number of random numbers to be generated.	1 to 6
	Range Start	Specifies the lower limit of the random number generation range.	0, 1 to 98
	Range End	Specifies the upper limit of the random number generation range.	1 to 40 to 99
	Repeat^*2	Specifies whether the same value can be repeatedly generated (On) or not (Off). “” is displayed in the upper left corner of the result screen when On is selected for repeat.	On, Off

Setting Items Common to All Simulation Types

Item	Description	Setting^*1
Refresh Freq	Specifies how often (in terms of the number of results) the result screen should be refreshed. Specifying “After Last Trial” here causes the screen to be refreshed after the last trial.	After 1 Trial, After 20 Trials, After 50 Trials, After Last Trial
Random Seed	Specifies a seed value to use for generation of pseudo-random numbers.	1 to 99999

Underlined settings indicate initial defaults.

When Off is specified for the Repeat setting, the random number range must be set to a value that is greater than the number of random numbers to be generated.

Note

To restore all Setup tab setting items to their initial default settings, select T > [Initialize].

For Coin Toss, Dice Roll, Spinner, and Marble Grab, you can specify an occurrence rate bias (for example, probability that Coin Toss will produce heads or tails). See Specifying an Occurrence Rate Bias (Bias) for details.

Step 3: Run the simulation and display its results (Result tab).

On the Setup tab, press >, or highlight and then press O.

The results of the simulation are displayed on the Result tab. See Using the Result Tab for information about the results displayed for each simulation type.

Example simulation result display:

Dice Roll

Random Numbers

The leftmost column of the table shows the number of trials.

You can use u and d to scroll a table up and down. You can use l and r to scroll a graph left and right.

The table below shows operations you can perform on the Result tab.

To do this:	Perform this operation:
Re-run a simulation for the same number of trials as the original	Press O.
Re-run the simulation for a specified number of trials	On the dialog box that appears when you press a number key or select T > [Increase trials (n)], input the desired number of trials and then press O.
Select Table, Graph, or Graph + Table as result display format^*1	Select T > [Results Display].
Store the simulation results to a list variable	Select T > [Store].^*2
Delete the current simulation results and return to the Setup tab	Select T > [Delete].
Display a crosshair pointer () and read the bar chart values (frequency and probability)^*3	Select T > [Trace].

This operation can be performed for Coin Toss, Dice Roll, Spinner, and Marble Grab.

See To store simulation results to a list variable for details.

This operation can be performed while T > [Results Display] > [Graph] is selected. For more information, see To read bar chart frequency and probability values.

To return to the Setup tab, press < (or b).

In response to a dialog box that appears asking if you want to delete the current simulation results, select [OK].

Specifying an Occurrence Rate Bias (Bias)

In real life, one side of a coin tends to appear more often than the other side, and one number of a die tends to appear more often than the others. This is due to the physical shape of the coin or die, or an offset of its center of gravity. Also, the number of Marble Grab marbles may differ depending on the marble type. This kind of occurrence rate bias can be specified for each simulation type. Occurrence rate bias can be specified for Coin Toss, Dice Roll, Spinner, and Marble Grab.

To specify Bias for Coin Toss, Dice Roll, or Spinner

Display the Setup tab for Coin Toss, Dice Roll, or Spinner.

Select T > [Bias].

This displays a screen for changing the weight (Weight) and probability (Prob) of a particular outcome.

Change the Weight or Prob value for each outcome.

Weight:	Specify a value between 0 and 999 (initial default: 1). Changing the Weight of one outcome causes the Prob values of all outcomes to be recalculated accordingly.
Prob:	Specify a value with up to four decimal places. Changing the Prob of one outcome causes the Prob and Weight values of all outcomes to be recalculated accordingly.

To initialize all Weight and Prob values, select T > [Initialize].

After everything is the way you want, press b to close the editing screen.

To specify Bias for Marble Grab

Display the Setup tab for Marble Grab.

Select T > [Bias].

This displays a screen for editing the number of each type of marble.

For each marble type, specify the number of marbles between 0 and 999 (initial default: 10).

To initialize this setting, select T > [Initialize].

After everything is the way you want, press b to close the editing screen.

Using the Result Tab

The table below shows the Result tab contents for each simulation type.

Type		Table	Graph
Coin Toss	1 coin	Cumulative number of heads over multiple tosses	Head/tail frequencies over multiple tosses
Coin Toss	2 coins/3 coins	Number of heads for a single toss	Cumulative frequencies of number of heads over multiple tosses
Dice Roll	1 die	Number produced by a single roll	Frequencies of each number over multiple rolls
Dice Roll	2 dice/3 dice	Total of numbers produced by a single roll	Frequencies of roll totals over multiple rolls
Spinner		Spinner number by a single spin	Frequencies of each number over multiple spins
Marble Grab		Types of marbles for a single grab	Frequencies of each type of marble over multiple grabs
Card Draw		Rank and suit of drawn card	-
Random Numbers		Generated random integer	-

To store simulation results to a list variable

Example 1: To store the results of a simulation of 20 tosses of 3 coins to a list variable

Display the Setup tab for Coin Toss.

Highlight [‎# of Trials], input “20” and then press O.

Highlight [Coins] and then press O.

On the menu that appears, select [3] and then press O.

Press >.

The results of the simulation are displayed on the Result tab.

Select T > [Store].

This displays a screen for specifying the store destination list variable.

If necessary, change the list variable number to specify the destination where each row of data should be stored.

Highlight the line you wish to change and then press O.
Use the dialog box that appears to input a list number and then press O.

Inputting a list number that is already specified in another line causes the message “Data is in use” to appear. Press O to close the message and then specify a different list number.

Highlight and then press O.

This stores the simulation results to the specified list variable.

Note

You can check what has been stored by starting up the Statistics app and displaying the List Editor.

For Card Draw results, the Value (rank) and Suit results are stored in separate lists. Also, the A, J, Q, and K ranks and the heart, club, spade, and diamond suits are stored as the values shown below.

A = 1, J = 11, Q = 12, K = 13

Hearts = 1, Clubs = 2, Spades = 3, Diamonds = 4

To read bar chart frequency and probability values

Example 2: To display a full-screen bar graph of the simulation results of Example 1 and display the frequency and probability values for each bar

Perform steps 1 through 5 of Example 1.

Select T > [Results Display] > [Graph].

This displays a full-screen bar chart.

Select T > [Trace].

This causes a crosshair pointer ( +pointer ) to appear at the left-most bar, along with the frequency (Freq) and probability (Prob) values at the top of the screen.

You can use l and r to move the pointer to the left and right.

To clear the pointer from the bar chart, press b.

Prob Sim App Settings Menu Items

The Settings menu items described below are specific to the Prob Sim app.

S > [Maximum Scale] …	Specifies whether the maximum value of the vertical axis on the Result tab is shown or hidden on the graph.
S > [Animation] …	Specifies whether an animation should be displayed before results when a simulation is performed.