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Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for both dice) is between 3 and 12. Die 2 Die 1 1 3. 6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) 1 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) 4. 6. ... There are different ways the sum can be between 3 and 12. 41

Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for both dice) is between 3 and 12. Die 2 Die 1 1 3. 6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) 1 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) 4. 6. ... There are different ways the sum can be between 3 and 12. 41

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Dice Outcome Table Analysis** When rolling two six-sided dice, each labeled as Die 1 and Die 2, there are 36 possible outcomes. This can be visualized in the following table, where each cell represents a pair of outcomes from Die 1 and Die 2: | Die 1\Die 2 | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|-------|-------|-------|-------|-------|-------| | **1** | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) | | **2** | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) | | **3** | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) | | **4** | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) | | **5** | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) | | **6** | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) | The task is to determine the number of outcomes where the sum of the numbers on both dice is between 3 and 12. **Calculation Explanation:** - The minimum sum is 2 (from (1,1)) and the maximum sum is 12 (from (6,6)). - You need to count all outcomes where the sum is between 3 and 12 inclusive. **Counting Sums from 3 to 12:** 1. **Sum = 3**: (1,2), (2,1) 2. **Sum = 4**: (1,3), (2,2), (3,1) 3. **Sum = 5
Transcribed Image Text:**Dice Outcome Table Analysis** When rolling two six-sided dice, each labeled as Die 1 and Die 2, there are 36 possible outcomes. This can be visualized in the following table, where each cell represents a pair of outcomes from Die 1 and Die 2: | Die 1\Die 2 | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|-------|-------|-------|-------|-------|-------| | **1** | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) | | **2** | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) | | **3** | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) | | **4** | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) | | **5** | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) | | **6** | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) | The task is to determine the number of outcomes where the sum of the numbers on both dice is between 3 and 12. **Calculation Explanation:** - The minimum sum is 2 (from (1,1)) and the maximum sum is 12 (from (6,6)). - You need to count all outcomes where the sum is between 3 and 12 inclusive. **Counting Sums from 3 to 12:** 1. **Sum = 3**: (1,2), (2,1) 2. **Sum = 4**: (1,3), (2,2), (3,1) 3. **Sum = 5
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