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
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ISBN:9781119256830
Author:Amos Gilat
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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.
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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