Two dice are rolled. What is the probability of getting a sum equals 7? Probability = (Round to 4 decimal places)
Two dice are rolled. What is the probability of getting a sum equals 7? Probability = (Round to 4 decimal places)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 78E
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need help with this please!
![### Probability of Rolling a Sum of 7 with Two Dice
When two dice are rolled, each die has 6 faces resulting in a total of 36 possible outcomes. The image above illustrates all possible combinations of rolling two dice. Each row and column represent the outcome of each die, with each cell depicting the sum of the outcomes.
**Diagrams Explanation:**
- The grid is a 6x6 matrix representing all possible outcomes when rolling two dice.
- Each cell shows a pair of dice with the sum of their faces.
- The pairs that result in a sum of 7 are specially marked in red for easy identification.
**Identifying Favorable Outcomes:**
The following are combinations of dice rolls that result in a sum of 7:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are 6 such combinations.
**Calculating Probability:**
The probability \(P\) of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[ P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values:
\[ P(\text{sum of 7}) = \frac{6}{36} = \frac{1}{6} \approx 0.1667 \]
**Probability =** ` 0.1667 ` (Rounded to 4 decimal places)
Students can use this explanation to understand how to analyze the outcomes of rolling two dice and calculate the probability of obtaining a specific sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2Fe9cef036-c5bd-4435-83a9-c1ff142b97f4%2Fn8q2h_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability of Rolling a Sum of 7 with Two Dice
When two dice are rolled, each die has 6 faces resulting in a total of 36 possible outcomes. The image above illustrates all possible combinations of rolling two dice. Each row and column represent the outcome of each die, with each cell depicting the sum of the outcomes.
**Diagrams Explanation:**
- The grid is a 6x6 matrix representing all possible outcomes when rolling two dice.
- Each cell shows a pair of dice with the sum of their faces.
- The pairs that result in a sum of 7 are specially marked in red for easy identification.
**Identifying Favorable Outcomes:**
The following are combinations of dice rolls that result in a sum of 7:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are 6 such combinations.
**Calculating Probability:**
The probability \(P\) of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[ P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values:
\[ P(\text{sum of 7}) = \frac{6}{36} = \frac{1}{6} \approx 0.1667 \]
**Probability =** ` 0.1667 ` (Rounded to 4 decimal places)
Students can use this explanation to understand how to analyze the outcomes of rolling two dice and calculate the probability of obtaining a specific sum.
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