If Two Dice Are Rolled One Time, Find The Probability Of Getting These Results. Enter Your Answers As Fractions Or As Decimals Rounded To 3 Decimal Places.Part 1 Of 4(a) A Sum Of 11${ P(\text{sum Of 11}) = \square }$
Introduction
Rolling two dice is a classic probability experiment that has been studied extensively in mathematics. The outcome of rolling two dice can result in a wide range of possible sums, from 2 to 12. In this article, we will focus on finding the probability of getting a specific sum, namely 11, when two dice are rolled one time.
The Basics of Dice Rolling
Before we dive into the calculations, let's review the basics of rolling two dice. Each die has six faces, numbered from 1 to 6. When two dice are rolled, there are a total of 36 possible outcomes, as each die has 6 possible outcomes and there are two dice.
Calculating the Probability of Getting a Sum of 11
To calculate the probability of getting a sum of 11, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 11, and divide it by the total number of possible outcomes.
Favorable Outcomes
The favorable outcomes for getting a sum of 11 are:
- Die 1: 5, Die 2: 6
- Die 1: 6, Die 2: 5
There are only two favorable outcomes where the sum is 11.
Total Number of Possible Outcomes
As mentioned earlier, there are a total of 36 possible outcomes when two dice are rolled.
Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability of getting a sum of 11.
P(sum of 11) = Number of favorable outcomes / Total number of possible outcomes = 2 / 36 = 1/18 = 0.0556 (rounded to 4 decimal places)
Conclusion
In this article, we calculated the probability of getting a sum of 11 when two dice are rolled one time. We found that the probability is 1/18 or 0.0556 (rounded to 4 decimal places). This result can be useful in various applications, such as games of chance or probability experiments.
Part 2: Calculating the Probability of Getting a Sum of 12
In the next part of this series, we will calculate the probability of getting a sum of 12 when two dice are rolled one time.
Calculating the Probability of Getting a Sum of 12
To calculate the probability of getting a sum of 12, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 12, and divide it by the total number of possible outcomes.
Favorable Outcomes
The favorable outcomes for getting a sum of 12 are:
- Die 1: 6, Die 2: 6
There is only one favorable outcome where the sum is 12.
Total Number of Possible Outcomes
As mentioned earlier, there are a total of 36 possible outcomes when two dice are rolled.
Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability of getting a sum of 12.
P(sum of 12) = Number of favorable outcomes / Total number of possible outcomes = 1 / 36 = 0.0278 (rounded to 4 decimal places)
Conclusion
In this article, we calculated the probability of getting a sum of 12 when two dice are rolled one time. We found that the probability is 1/36 or 0.0278 (rounded to 4 decimal places). This result can be useful in various applications, such as games of chance or probability experiments.
Part 3: Calculating the Probability of Getting a Sum of 10
In the next part of this series, we will calculate the probability of getting a sum of 10 when two dice are rolled one time.
Calculating the Probability of Getting a Sum of 10
To calculate the probability of getting a sum of 10, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 10, and divide it by the total number of possible outcomes.
Favorable Outcomes
The favorable outcomes for getting a sum of 10 are:
- Die 1: 4, Die 2: 6
- Die 1: 5, Die 2: 5
- Die 1: 6, Die 2: 4
There are three favorable outcomes where the sum is 10.
Total Number of Possible Outcomes
As mentioned earlier, there are a total of 36 possible outcomes when two dice are rolled.
Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability of getting a sum of 10.
P(sum of 10) = Number of favorable outcomes / Total number of possible outcomes = 3 / 36 = 1/12 = 0.0833 (rounded to 4 decimal places)
Conclusion
In this article, we calculated the probability of getting a sum of 10 when two dice are rolled one time. We found that the probability is 1/12 or 0.0833 (rounded to 4 decimal places). This result can be useful in various applications, such as games of chance or probability experiments.
Part 4: Calculating the Probability of Getting a Sum of 9
In the final part of this series, we will calculate the probability of getting a sum of 9 when two dice are rolled one time.
Calculating the Probability of Getting a Sum of 9
To calculate the probability of getting a sum of 9, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 9, and divide it by the total number of possible outcomes.
Favorable Outcomes
The favorable outcomes for getting a sum of 9 are:
- Die 1: 3, Die 2: 6
- Die 1: 4, Die 2: 5
- Die 1: 5, Die 2: 4
- Die 1: 6, Die 2: 3
There are four favorable outcomes where the sum is 9.
Total Number of Possible Outcomes
As mentioned earlier, there are a total of 36 possible outcomes when two dice are rolled.
Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability of getting a sum of 9.
P(sum of 9) = Number of favorable outcomes / Total number of possible outcomes = 4 / 36 = 1/9 = 0.1111 (rounded to 4 decimal places)
Conclusion
In this article, we calculated the probability of getting a sum of 9 when two dice are rolled one time. We found that the probability is 1/9 or 0.1111 (rounded to 4 decimal places). This result can be useful in various applications, such as games of chance or probability experiments.
Conclusion
In this series, we calculated the probability of getting various sums when two dice are rolled one time. We found that the probabilities are:
- P(sum of 11) = 1/18 = 0.0556 (rounded to 4 decimal places)
- P(sum of 12) = 1/36 = 0.0278 (rounded to 4 decimal places)
- P(sum of 10) = 1/12 = 0.0833 (rounded to 4 decimal places)
- P(sum of 9) = 1/9 = 0.1111 (rounded to 4 decimal places)
Q&A: Frequently Asked Questions about Dice Rolling
Q: What is the probability of getting a sum of 7 when two dice are rolled?
A: To calculate the probability of getting a sum of 7, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 7, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 7 are:
- Die 1: 1, Die 2: 6
- Die 1: 2, Die 2: 5
- Die 1: 3, Die 2: 4
- Die 1: 4, Die 2: 3
- Die 1: 5, Die 2: 2
- Die 1: 6, Die 2: 1
There are 6 favorable outcomes where the sum is 7. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 7 is:
P(sum of 7) = Number of favorable outcomes / Total number of possible outcomes = 6 / 36 = 1/6 = 0.1667 (rounded to 4 decimal places)
Q: What is the probability of getting a sum of 5 when two dice are rolled?
A: To calculate the probability of getting a sum of 5, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 5, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 5 are:
- Die 1: 1, Die 2: 4
- Die 1: 2, Die 2: 3
- Die 1: 3, Die 2: 2
- Die 1: 4, Die 2: 1
There are 4 favorable outcomes where the sum is 5. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 5 is:
P(sum of 5) = Number of favorable outcomes / Total number of possible outcomes = 4 / 36 = 1/9 = 0.1111 (rounded to 4 decimal places)
Q: What is the probability of getting a sum of 3 when two dice are rolled?
A: To calculate the probability of getting a sum of 3, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 3, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 3 are:
- Die 1: 1, Die 2: 2
- Die 1: 2, Die 2: 1
There are 2 favorable outcomes where the sum is 3. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 3 is:
P(sum of 3) = Number of favorable outcomes / Total number of possible outcomes = 2 / 36 = 1/18 = 0.0556 (rounded to 4 decimal places)
Q: What is the probability of getting a sum of 2 when two dice are rolled?
A: To calculate the probability of getting a sum of 2, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 2, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 2 are:
- Die 1: 1, Die 2: 1
There is 1 favorable outcome where the sum is 2. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 2 is:
P(sum of 2) = Number of favorable outcomes / Total number of possible outcomes = 1 / 36 = 0.0278 (rounded to 4 decimal places)
Q: What is the probability of getting a sum of 12 when two dice are rolled?
A: To calculate the probability of getting a sum of 12, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 12, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 12 are:
- Die 1: 6, Die 2: 6
There is 1 favorable outcome where the sum is 12. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 12 is:
P(sum of 12) = Number of favorable outcomes / Total number of possible outcomes = 1 / 36 = 0.0278 (rounded to 4 decimal places)
Q: What is the probability of getting a sum of 11 when two dice are rolled?
A: To calculate the probability of getting a sum of 11, we need to count the number of favorable outcomes, i.e., the number of outcomes where the sum is 11, and divide it by the total number of possible outcomes. The favorable outcomes for getting a sum of 11 are:
- Die 1: 5, Die 2: 6
- Die 1: 6, Die 2: 5
There are 2 favorable outcomes where the sum is 11. The total number of possible outcomes is 36. Therefore, the probability of getting a sum of 11 is:
P(sum of 11) = Number of favorable outcomes / Total number of possible outcomes = 2 / 36 = 1/18 = 0.0556 (rounded to 4 decimal places)
Conclusion
In this Q&A article, we answered frequently asked questions about dice rolling and probability. We calculated the probabilities of getting various sums when two dice are rolled, including sums of 2, 3, 5, 7, 11, and 12. These results can be useful in various applications, such as games of chance or probability experiments.