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30. Rolling Two Dice Using the sample space for tossing two dice, construct a probability distribution for the sums 2 through 12.

30. Rolling Two Dice Using the sample space for tossing two dice, construct a probability distribution for the sums 2 through 12.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**30. Rolling Two Dice** Using the sample space for tossing two dice, construct a probability distribution for the sums 2 through 12. --- ### Explanation When rolling two six-sided dice, each die has faces numbered from 1 to 6. The sample space consists of all possible pairs of numbers from the first and second die, which totals to 36 possible outcomes (since 6 x 6 = 36). To construct a probability distribution for the sums of the two dice (ranging from 2 to 12), we follow these steps: 1. **List Possible Sums**: The possible sums when rolling two dice are the integers from 2 (1+1) to 12 (6+6). 2. **Count Outcomes for Each Sum**: Determine how many combinations produce each sum. - Sum of 2: 1 outcome (1+1) - Sum of 3: 2 outcomes (1+2, 2+1) - Sum of 4: 3 outcomes (1+3, 2+2, 3+1) - Sum of 5: 4 outcomes (1+4, 2+3, 3+2, 4+1) - Sum of 6: 5 outcomes (1+5, 2+4, 3+3, 4+2, 5+1) - Sum of 7: 6 outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) - Sum of 8: 5 outcomes (2+6, 3+5, 4+4, 5+3, 6+2) - Sum of 9: 4 outcomes (3+6, 4+5, 5+4, 6+3) - Sum of 10: 3 outcomes (4+6, 5+5, 6+4) - Sum of 11: 2 outcomes (5+6, 6+5) - Sum of 12: 1 outcome (6+6) 3. **Calculate Probabilities**: The probability of each sum is the number of favorable outcomes divided by the total number of outcomes (36). 4. **Create Probability Distribution**: Prepare a table showing each sum
Transcribed Image Text:**30. Rolling Two Dice** Using the sample space for tossing two dice, construct a probability distribution for the sums 2 through 12. --- ### Explanation When rolling two six-sided dice, each die has faces numbered from 1 to 6. The sample space consists of all possible pairs of numbers from the first and second die, which totals to 36 possible outcomes (since 6 x 6 = 36). To construct a probability distribution for the sums of the two dice (ranging from 2 to 12), we follow these steps: 1. **List Possible Sums**: The possible sums when rolling two dice are the integers from 2 (1+1) to 12 (6+6). 2. **Count Outcomes for Each Sum**: Determine how many combinations produce each sum. - Sum of 2: 1 outcome (1+1) - Sum of 3: 2 outcomes (1+2, 2+1) - Sum of 4: 3 outcomes (1+3, 2+2, 3+1) - Sum of 5: 4 outcomes (1+4, 2+3, 3+2, 4+1) - Sum of 6: 5 outcomes (1+5, 2+4, 3+3, 4+2, 5+1) - Sum of 7: 6 outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) - Sum of 8: 5 outcomes (2+6, 3+5, 4+4, 5+3, 6+2) - Sum of 9: 4 outcomes (3+6, 4+5, 5+4, 6+3) - Sum of 10: 3 outcomes (4+6, 5+5, 6+4) - Sum of 11: 2 outcomes (5+6, 6+5) - Sum of 12: 1 outcome (6+6) 3. **Calculate Probabilities**: The probability of each sum is the number of favorable outcomes divided by the total number of outcomes (36). 4. **Create Probability Distribution**: Prepare a table showing each sum
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