If a pair of dice is rolled, what is the probability of a double? What is the probability of rolling a sum of 11 or more?
If a pair of dice is rolled, what is the probability of a double? What is the probability of rolling a sum of 11 or more?
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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![**Question 6**
If a pair of dice is rolled, what is the probability of a double? What is the probability of rolling a sum of 11 or more?
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For those studying probability, understanding the outcomes of rolling two dice can be both fascinating and educational. When you roll two six-sided dice, numerous outcomes are possible.
**Probability of a Double:**
A double occurs when both dice show the same number. The possible doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). Since there are 6 favorable outcomes and 36 possible outcomes in total (since each die has 6 sides, 6 x 6 = 36 combinations), the probability of rolling a double is:
\[ \frac{6}{36} = \frac{1}{6} \]
**Probability of Rolling a Sum of 11 or More:**
To find this probability, consider the possible combinations:
- A sum of 11 can be achieved with the following combinations: (5,6) and (6,5).
- A sum of 12 is possible with (6,6).
This gives a total of 3 favorable outcomes for a sum of 11 or more. Therefore, the probability is:
\[ \frac{3}{36} = \frac{1}{12} \]
These calculations are essential in fields like statistics, gaming, and any scenario involving probabilistic prediction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98b6e310-08ba-4e1d-a9bc-704b45d2ce6c%2F179f28c5-4400-4bbb-be5d-ed56ec8b5259%2Fnijfui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6**
If a pair of dice is rolled, what is the probability of a double? What is the probability of rolling a sum of 11 or more?
---
For those studying probability, understanding the outcomes of rolling two dice can be both fascinating and educational. When you roll two six-sided dice, numerous outcomes are possible.
**Probability of a Double:**
A double occurs when both dice show the same number. The possible doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). Since there are 6 favorable outcomes and 36 possible outcomes in total (since each die has 6 sides, 6 x 6 = 36 combinations), the probability of rolling a double is:
\[ \frac{6}{36} = \frac{1}{6} \]
**Probability of Rolling a Sum of 11 or More:**
To find this probability, consider the possible combinations:
- A sum of 11 can be achieved with the following combinations: (5,6) and (6,5).
- A sum of 12 is possible with (6,6).
This gives a total of 3 favorable outcomes for a sum of 11 or more. Therefore, the probability is:
\[ \frac{3}{36} = \frac{1}{12} \]
These calculations are essential in fields like statistics, gaming, and any scenario involving probabilistic prediction.
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