HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 4.

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HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 4 Technology

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.1: Using a TI-83/84 Plus Calculator to Calculate a Factorial Use a TI-83/84 Plus calculator to calculate 9! Solution Press, then, and then select PRB and option 4:!. Press. As you can see in the screenshot on the right, 9! = 362,880.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.2: Using a TI-83/84 Plus Calculator to Calculate the Number of Combinations Use a TI-83/84 Plus calculator to calculate 15 C 9. Solution Enter 15, and then press. Next, scroll over to PRB and choose option 3:nCr. Then enter 9 and press.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.2: Using a TI-83/84 Plus Calculator to Calculate the Number of Combinations (cont.) The screenshot on the right shows that 15 C 9 = 5005.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.3: Using a TI-83/84 Plus Calculator to Calculate the Number of Permutations Use a TI-83/84 Plus calculator to calculate 11 P 4. Solution First, enter 11 and then press. Next, scroll over to PRB and choose option 2:nPr. Then enter 4 and press.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.3: Using a TI-83/84 Plus Calculator to Calculate the Number of Permutations (cont.) As shown in the screenshot on the right, 11 P 4 = 7920.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Calculate the Probability of Several Independent Events A coin is flipped, a die is rolled, and a card is drawn from a deck. Use Microsoft Excel to find the probability of getting a tail on the coin, rolling a 5 on the die, and drawing a heart from the deck of cards. Solution First enter the data in an Excel worksheet as shown here.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Calculate the Probability of Several Independent Events (cont.) Then in cell B4, divide B2 by B3. To do this, type the formula =B2/B3. Copy the formula from cell B4 into C4 and D4. Now the probabilities for each event are listed in row 4. Remember, when events are independent we multiply the probabilities of each event occurring with each other. Therefore, in cell E4, multiply the cells B4 through D4 by typing =B4*C4*D4.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Calculate the Probability of Several Independent Events (cont.) The result, shown in the following screenshot, will be the probability of getting a tail on the coin, a 5 on the die, and drawing a heart from the deck of cards, which is approximately

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate a Factorial Use M INITAB to calculate 10! Solution Go to Calc ► Calculator. Type C1 in the box after Store result in variable. Select Factorial under All functions, and then type 10 to replace “number of items” in the expression. Then click OK; the result, , will be displayed in row 1 of column C1. Thus, 10! = 3,628,800.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate a Factorial (cont.)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.6: Using M INITAB to Calculate the Number of Combinations Use M INITAB to calculate 15 C 13. Solution Go to Calc ► Calculator. Type C1 in the box after Store result in variable. Select Combinations under All functions. Type 15 to replace “number of items” and type 13 to replace “number to choose” in the expression. Then click OK; the result, 105, will be displayed in row 1 of column C1. Thus, 15 C 13 = 105.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.6: Using M INITAB to Calculate the Number of Combinations (cont.)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.7: Using M INITAB to Calculate the Number of Permutations Use M INITAB to calculate 18 P 7. Solution Go to Calc ► Calculator. Type C1 in the box after Store result in variable. Select Permutations under All functions. Type 18 to replace “number of items” and type 7 to replace “number to choose” in the expression. Then click OK; the result, , will be displayed in row 1 of column C1. Thus, 18 P 7 = 160,392,960.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.7: Using M INITAB to Calculate the Number of Permutations (cont.)