图国 图 图国 围 围网 Two dice are rolled. What is the probability of getting a sum equals 7? Probability = 3 x (Round to 4 decimal places) Check Answer

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
**Title:** Probability of Rolling a Sum of 7 with Two Dice

**Description:**

In this exercise, we explore the probability of obtaining a sum of 7 when rolling two six-sided dice. Each die has faces numbered from 1 to 6.

**Diagram Explanation:**

The diagram above displays all possible outcomes when two dice are rolled. There are 36 possible combinations, as each die can land on any of its 6 faces.

**Combinations for Sum of 7:**

To find the probability of rolling a sum of 7, identify the following combinations from the diagram:

1. Die 1: 1, Die 2: 6
2. Die 1: 2, Die 2: 5
3. Die 1: 3, Die 2: 4
4. Die 1: 4, Die 2: 3
5. Die 1: 5, Die 2: 2
6. Die 1: 6, Die 2: 1

There are 6 favorable outcomes.

**Probability Calculation:**

The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Therefore:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{6}{36} = \frac{1}{6} \approx 0.1667 \]

*Note: Round to 4 decimal places as instructed.*

**Interactive Component:**

- Enter the calculated probability in the box provided.
- Click "Check Answer" to verify your solution.

**End of Description**
Transcribed Image Text:**Title:** Probability of Rolling a Sum of 7 with Two Dice **Description:** In this exercise, we explore the probability of obtaining a sum of 7 when rolling two six-sided dice. Each die has faces numbered from 1 to 6. **Diagram Explanation:** The diagram above displays all possible outcomes when two dice are rolled. There are 36 possible combinations, as each die can land on any of its 6 faces. **Combinations for Sum of 7:** To find the probability of rolling a sum of 7, identify the following combinations from the diagram: 1. Die 1: 1, Die 2: 6 2. Die 1: 2, Die 2: 5 3. Die 1: 3, Die 2: 4 4. Die 1: 4, Die 2: 3 5. Die 1: 5, Die 2: 2 6. Die 1: 6, Die 2: 1 There are 6 favorable outcomes. **Probability Calculation:** The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Therefore: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{6}{36} = \frac{1}{6} \approx 0.1667 \] *Note: Round to 4 decimal places as instructed.* **Interactive Component:** - Enter the calculated probability in the box provided. - Click "Check Answer" to verify your solution. **End of Description**
Expert Solution
Step 1

Step 1:

The sample space after rolling two dice is given as,

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

        (2,1 ), (2,2), (2,3), (2,4), (2,5), (2,6),

        (3,1 ), (3,2), (3,3), (3,4), (3,5), (3,6),

        (4,1 ), (4,2), (4,3), (4,4), (4,5), (4,6),

        (5,1 ), (5,2), (5,3), (5,4), (5,5), (5,6),

        (6,1 ), (6,2), (6,3), (6,4), (6,5), (6,6)}

Thus,

n(S) = 36

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman