BOB Two dice are rolled. What is the probability of getting a sum equals 7? (Round to 4 decimal places) Probability -
BOB Two dice are rolled. What is the probability of getting a sum equals 7? (Round to 4 decimal places) Probability -
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
Related questions
Question
![**Probability of Rolling a Sum of 7 with Two Dice**
When two dice are rolled, there are a number of possible outcomes. The diagram above displays all possible outcomes of rolling two six-sided dice. Each die is represented with numbers 1 through 6, and every possible combination of the two dice is shown.
**Explanation of the Diagram:**
- The diagram consists of a 6x6 grid, displaying all 36 possible outcomes when two dice are rolled.
- Each cell in the grid represents a unique combination of results from the two dice. The first die's result is given by the row, and the second die's result is given by the column.
**Finding the Probability of Getting a Sum of 7:**
To find the probability of getting a sum of 7, we need to:
1. Identify all the pairs of dice that sum up to 7.
2. Count these favorable outcomes.
3. Divide the number of favorable outcomes by the total number of possible outcomes (which is 36).
**Outcomes that Result in a Sum of 7:**
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
Thus, there are 6 favorable outcomes.
**Calculating the Probability:**
The probability \( P \) of rolling a sum of 7 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[ P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \]
**Expressing the Probability:**
Rounded to 4 decimal places, the probability of rolling a sum of 7 is:
\[ \boxed{0.1667} \]
**Interactive Element for Students:**
Students can enter the calculated probability in the box provided:
\[ \text{Probability} = \boxed{} \text{ (Round to 4 decimal places)} \]
This exercise helps students understand the fundamentals of calculating probabilities with a clear visual aid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2F0b47597b-ed95-4dea-8a39-b8fe8b71ba62%2Fkny30ym_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability of Rolling a Sum of 7 with Two Dice**
When two dice are rolled, there are a number of possible outcomes. The diagram above displays all possible outcomes of rolling two six-sided dice. Each die is represented with numbers 1 through 6, and every possible combination of the two dice is shown.
**Explanation of the Diagram:**
- The diagram consists of a 6x6 grid, displaying all 36 possible outcomes when two dice are rolled.
- Each cell in the grid represents a unique combination of results from the two dice. The first die's result is given by the row, and the second die's result is given by the column.
**Finding the Probability of Getting a Sum of 7:**
To find the probability of getting a sum of 7, we need to:
1. Identify all the pairs of dice that sum up to 7.
2. Count these favorable outcomes.
3. Divide the number of favorable outcomes by the total number of possible outcomes (which is 36).
**Outcomes that Result in a Sum of 7:**
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
Thus, there are 6 favorable outcomes.
**Calculating the Probability:**
The probability \( P \) of rolling a sum of 7 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[ P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \]
**Expressing the Probability:**
Rounded to 4 decimal places, the probability of rolling a sum of 7 is:
\[ \boxed{0.1667} \]
**Interactive Element for Students:**
Students can enter the calculated probability in the box provided:
\[ \text{Probability} = \boxed{} \text{ (Round to 4 decimal places)} \]
This exercise helps students understand the fundamentals of calculating probabilities with a clear visual aid.
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