When Rolling A 6-sided Die Twice, Determine The Probability $P($sum Of 6$)$.A. $\frac{12}{36}$B. $\frac{7}{36}$C. $\frac{5}{36}$D. $\frac{2}{6}$

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Introduction

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. In this article, we will explore the probability of rolling a 6-sided die twice and obtaining a sum of 6. We will analyze the possible outcomes, calculate the probability, and compare it with the given options.

Understanding the Problem

When rolling a 6-sided die twice, there are a total of 36 possible outcomes. Each die has 6 possible outcomes, and since we are rolling two dice, the total number of outcomes is 6 x 6 = 36. We want to find the probability of obtaining a sum of 6.

Possible Outcomes

To determine the possible outcomes, we need to consider all the combinations of the two dice. We can represent the outcomes as (die 1, die 2), where each die can take a value from 1 to 6.

Here are the possible outcomes:

Die 1 Die 2 Sum
1 1 2
1 2 3
1 3 4
1 4 5
1 5 6
1 6 7
2 1 3
2 2 4
2 3 5
2 4 6
2 5 7
2 6 8
3 1 4
3 2 5
3 3 6
3 4 7
3 5 8
3 6 9
4 1 5
4 2 6
4 3 7
4 4 8
4 5 9
4 6 10
5 1 6
5 2 7
5 3 8
5 4 9
5 5 10
5 6 11
6 1 7
6 2 8
6 3 9
6 4 10
6 5 11
6 6 12

Calculating the Probability

We want to find the probability of obtaining a sum of 6. From the table above, we can see that there are 5 outcomes that result in a sum of 6:

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

There are a total of 36 possible outcomes, and 5 of them result in a sum of 6. Therefore, the probability of obtaining a sum of 6 is:

P(sum of 6) = Number of favorable outcomes / Total number of outcomes = 5 / 36

Conclusion

In this article, we have determined the probability of rolling a 6-sided die twice and obtaining a sum of 6. We have analyzed the possible outcomes, calculated the probability, and compared it with the given options. The correct answer is:

The final answer is: 536\boxed{\frac{5}{36}}

Comparison with Given Options

We can compare our answer with the given options:

  • A. 1236\frac{12}{36} = 13\frac{1}{3}
  • B. 736\frac{7}{36}
  • C. 536\frac{5}{36}
  • D. 26\frac{2}{6} = 13\frac{1}{3}

Our answer, 536\frac{5}{36}, is option C. Therefore, the correct answer is:

Introduction

In our previous article, we explored the probability of rolling a 6-sided die twice and obtaining a sum of 6. We analyzed the possible outcomes, calculated the probability, and compared it with the given options. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the total number of possible outcomes when rolling a 6-sided die twice?

A: The total number of possible outcomes is 6 x 6 = 36.

Q: How many outcomes result in a sum of 6?

A: There are 5 outcomes that result in a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

Q: What is the probability of obtaining a sum of 6?

A: The probability of obtaining a sum of 6 is 5/36.

Q: Can you explain why the probability is 5/36 and not 1/6?

A: The probability is 5/36 because there are 5 outcomes that result in a sum of 6 out of a total of 36 possible outcomes. If there were only 6 possible outcomes, the probability would be 1/6. However, in this case, there are 36 possible outcomes, and only 5 of them result in a sum of 6.

Q: What is the difference between the probability of obtaining a sum of 6 and the probability of obtaining a sum of 7?

A: The probability of obtaining a sum of 7 is 6/36 = 1/6, which is different from the probability of obtaining a sum of 6, which is 5/36.

Q: Can you explain why the probability of obtaining a sum of 7 is 1/6?

A: The probability of obtaining a sum of 7 is 1/6 because there are 6 outcomes that result in a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

Q: What is the relationship between the probability of obtaining a sum of 6 and the probability of obtaining a sum of 12?

A: The probability of obtaining a sum of 12 is 1/36, which is different from the probability of obtaining a sum of 6, which is 5/36.

Q: Can you explain why the probability of obtaining a sum of 12 is 1/36?

A: The probability of obtaining a sum of 12 is 1/36 because there is only 1 outcome that results in a sum of 12: (6, 6).

Conclusion

In this article, we have answered some frequently asked questions related to the probability of rolling a 6-sided die twice and obtaining a sum of 6. We have explained the total number of possible outcomes, the number of outcomes that result in a sum of 6, and the probability of obtaining a sum of 6. We have also compared the probability of obtaining a sum of 6 with the probability of obtaining a sum of 7 and the probability of obtaining a sum of 12.

Frequently Asked Questions

  • What is the total number of possible outcomes when rolling a 6-sided die twice?
  • How many outcomes result in a sum of 6?
  • What is the probability of obtaining a sum of 6?
  • Can you explain why the probability is 5/36 and not 1/6?
  • What is the difference between the probability of obtaining a sum of 6 and the probability of obtaining a sum of 7?
  • Can you explain why the probability of obtaining a sum of 7 is 1/6?
  • What is the relationship between the probability of obtaining a sum of 6 and the probability of obtaining a sum of 12?
  • Can you explain why the probability of obtaining a sum of 12 is 1/36?

Answers

  • The total number of possible outcomes is 6 x 6 = 36.
  • There are 5 outcomes that result in a sum of 6.
  • The probability of obtaining a sum of 6 is 5/36.
  • The probability is 5/36 because there are 5 outcomes that result in a sum of 6 out of a total of 36 possible outcomes.
  • The probability of obtaining a sum of 7 is 1/6, which is different from the probability of obtaining a sum of 6, which is 5/36.
  • The probability of obtaining a sum of 7 is 1/6 because there are 6 outcomes that result in a sum of 7.
  • The probability of obtaining a sum of 12 is 1/36, which is different from the probability of obtaining a sum of 6, which is 5/36.
  • The probability of obtaining a sum of 12 is 1/36 because there is only 1 outcome that results in a sum of 12.