Question

What is a simulation of a procedure such as the toss of a fair coin 10 Times?

How will you simulate the toss of a fair coin toss repeated 10 times on a Ti-84 plus?

What is a permutation of n different items or elements and state the permutation rule and it’s requirements.

What is a combination of n different items or elements and state the combination rule and it’s requirements.

What is the relationship between sampling without replacement and independence and how does that affect the computation of the probabilities of two successive events? How about sampling with replacement; does that lead to independent or dependent outcomes?

Thanks!

Answer 1

How to toss coins in Probability Simulation

To toss coins, follow these steps:

1. Start the Probability Simulation application and press [1] to select the Toss Coins option in the Main menu.

   You see the Toss Coins Home screen.

   To use the Toss Coins simulator after using another simulator, repeatedly press [Y=] until you see the Main menu, and then press [1] to select the Toss Coins simulator.

   

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

   The second picture shows the Settings editor. The Coins option lets you tell the application to toss 1, 2, or 3 coins each time it tosses coins.

   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 then press [ENTER] to select the option.

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

   The screen you see is similar to the third picture shown. If you are tossing more than one coin, the application requires that all of the coins be weighted in the same way. For example, if you want one coin to be twice as likely to land heads up and you are tossing three coins, then all three coins must be twice as likely to land heads up.

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 Toss Coins Home screen.

5. Press [WINDOW] to toss coins.

   

   You see a screen similar to the first or second picture shown here. If one coin was tossed only one time, then only one bar appears in the histogram.

6. Continue tossing coins.

   If in Step 2, you set Trial Set to a number greater than one, then after tossing the first set of coins, you see a screen similar to the first picture. Press [WINDOW] to toss more coins.

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

How to read the Toss Coins graph or table

The cumulative data from tossing coins 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 Toss Coins histogram and table:

• Toss Coins histogram: If you are tossing only one coin, the histogram displays the cumulative outcomes of tails and heads from repeated tossing of the coin. If you are tossing more than one coin, the histogram displays only cumulative outcomes of heads. For example, if you are tossing two coins, the histogram displays the outcomes of no heads, one head, or two heads.

• Toss Coins table: The number of the toss appears in the first column of the table. If only one coin is tossed, the second column contains the outcome (H for heads or T for tails) for that coin and the last column contains the cumulative number of heads.

  If more than one coin is tossed, the middle columns contain the outcome (H or T) for each coin and the last column contains the total number of heads for that particular toss of the coins.