Two Dice Are Thrown Simultaneously. Find The Probability That:a. Both Dice Have The Same Number.b. The Total Number On The Dice Is Greater Than A Certain Value (complete The Statement).c. The Sum Of Numbers On The Dice Is 9.d. Both Numbers On The Dice
Two Dice are Thrown Simultaneously: Exploring Probability
When two dice are thrown simultaneously, the outcome is a combination of the numbers obtained on each die. In this article, we will explore the probability of certain events occurring when two dice are thrown. We will calculate the probability of both dice having the same number, the total number on the dice being greater than a certain value, the sum of numbers on the dice being 9, and both numbers on the dice being different.
When two dice are thrown, there are 36 possible outcomes, as each die has 6 possible outcomes and there are two dice. To find the probability of both dice having the same number, we need to count the number of favorable outcomes.
| Die 1 | Die 2 | Favorable Outcome |
|---|---|---|
| 1 | 1 | Yes |
| 2 | 2 | Yes |
| 3 | 3 | Yes |
| 4 | 4 | Yes |
| 5 | 5 | Yes |
| 6 | 6 | Yes |
There are 6 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of both dice having the same number is:
P(Both Dice Have the Same Number) = 6/36 = 1/6
Let's say we want to find the probability of the total number on the dice being greater than 7. To do this, we need to count the number of favorable outcomes.
| Die 1 | Die 2 | Total | Favorable Outcome |
|---|---|---|---|
| 1 | 1 | 2 | No |
| 1 | 2 | 3 | No |
| 1 | 3 | 4 | No |
| 1 | 4 | 5 | No |
| 1 | 5 | 6 | No |
| 1 | 6 | 7 | No |
| 2 | 1 | 3 | No |
| 2 | 2 | 4 | No |
| 2 | 3 | 5 | No |
| 2 | 4 | 6 | No |
| 2 | 5 | 7 | No |
| 2 | 6 | 8 | Yes |
| 3 | 1 | 4 | No |
| 3 | 2 | 5 | No |
| 3 | 3 | 6 | No |
| 3 | 4 | 7 | No |
| 3 | 5 | 8 | Yes |
| 3 | 6 | 9 | Yes |
| 4 | 1 | 5 | No |
| 4 | 2 | 6 | No |
| 4 | 3 | 7 | No |
| 4 | 4 | 8 | Yes |
| 4 | 5 | 9 | Yes |
| 4 | 6 | 10 | Yes |
| 5 | 1 | 6 | No |
| 5 | 2 | 7 | No |
| 5 | 3 | 8 | Yes |
| 5 | 4 | 9 | Yes |
| 5 | 5 | 10 | Yes |
| 5 | 6 | 11 | Yes |
| 6 | 1 | 7 | No |
| 6 | 2 | 8 | Yes |
| 6 | 3 | 9 | Yes |
| 6 | 4 | 10 | Yes |
| 6 | 5 | 11 | Yes |
| 6 | 6 | 12 | Yes |
There are 15 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of the total number on the dice being greater than 7 is:
P(Total Number > 7) = 15/36 = 5/12
To find the probability of the sum of numbers on the dice being 9, we need to count the number of favorable outcomes.
| Die 1 | Die 2 | Sum | Favorable Outcome |
|---|---|---|---|
| 1 | 1 | 2 | No |
| 1 | 2 | 3 | No |
| 1 | 3 | 4 | No |
| 1 | 4 | 5 | No |
| 1 | 5 | 6 | No |
| 1 | 6 | 7 | No |
| 2 | 1 | 3 | No |
| 2 | 2 | 4 | No |
| 2 | 3 | 5 | No |
| 2 | 4 | 6 | No |
| 2 | 5 | 7 | No |
| 2 | 6 | 8 | No |
| 3 | 1 | 4 | No |
| 3 | 2 | 5 | No |
| 3 | 3 | 6 | No |
| 3 | 4 | 7 | No |
| 3 | 5 | 8 | No |
| 3 | 6 | 9 | Yes |
| 4 | 1 | 5 | No |
| 4 | 2 | 6 | No |
| 4 | 3 | 7 | No |
| 4 | 4 | 8 | No |
| 4 | 5 | 9 | Yes |
| 4 | 6 | 10 | No |
| 5 | 1 | 6 | No |
| 5 | 2 | 7 | No |
| 5 | 3 | 8 | No |
| 5 | 4 | 9 | Yes |
| 5 | 5 | 10 | No |
| 5 | 6 | 11 | No |
| 6 | 1 | 7 | No |
| 6 | 2 | 8 | No |
| 6 | 3 | 9 | Yes |
| 6 | 4 | 10 | No |
| 6 | 5 | 11 | No |
| 6 | 6 | 12 | No |
There are 4 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of the sum of numbers on the dice being 9 is:
P(Sum = 9) = 4/36 = 1/9
To find the probability of both numbers on the dice being different, we need to count the number of favorable outcomes.
| Die 1 | Die 2 | Favorable Outcome |
|---|---|---|
| 1 | 2 | Yes |
| 1 | 3 | Yes |
| 1 | 4 | Yes |
| 1 | 5 | Yes |
| 1 | 6 | Yes |
| 2 | 3 | Yes |
| 2 | 4 | Yes |
| 2 | 5 | Yes |
| 2 | 6 | Yes |
| 3 | 4 | Yes |
| 3 | 5 | Yes |
| 3 | 6 | Yes |
| 4 | 5 | Yes |
| 4 | 6 | Yes |
| 5 | 6 | Yes |
There are 15 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of both numbers on the dice being different is:
P(Both Numbers Different) = 15/36 = 5/12
In this article, we have explored the probability of certain events occurring when two dice are thrown simultaneously. We have calculated the probability of both dice having the same number, the total number on the dice
Two Dice are Thrown Simultaneously: Exploring Probability - Q&A
In our previous article, we explored the probability of certain events occurring when two dice are thrown simultaneously. We calculated the probability of both dice having the same number, the total number on the dice being greater than a certain value, the sum of numbers on the dice being 9, and both numbers on the dice being different. In this article, we will answer some frequently asked questions related to the topic.
A: To find the probability of getting a sum of 7, we need to count the number of favorable outcomes. The favorable outcomes are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are 6 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of getting a sum of 7 is:
P(Sum = 7) = 6/36 = 1/6
A: To find the probability of getting a total number greater than 10, we need to count the number of favorable outcomes. The favorable outcomes are:
- (5, 6)
- (6, 5)
- (6, 6)
There are 3 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of getting a total number greater than 10 is:
P(Total Number > 10) = 3/36 = 1/12
A: To find the probability of getting a sum of 11, we need to count the number of favorable outcomes. The favorable outcomes are:
- (5, 6)
- (6, 5)
There are 2 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of getting a sum of 11 is:
P(Sum = 11) = 2/36 = 1/18
A: To find the probability of getting a total number less than 5, we need to count the number of favorable outcomes. The favorable outcomes are:
- (1, 1)
- (1, 2)
- (2, 1)
- (1, 3)
- (3, 1)
- (2, 2)
There are 6 favorable outcomes, and the total number of possible outcomes is 36. Therefore, the probability of getting a total number less than 5 is:
P(Total Number < 5) = 6/36 = 1/6
A: To find the probability of getting a sum of 12, we need to count the number of favorable outcomes. The favorable outcome is:
- (6, 6)
There is 1 favorable outcome, and the total number of possible outcomes is 36. Therefore, the probability of getting a sum of 12 is:
P(Sum = 12) = 1/36
In this article, we have answered some frequently asked questions related to the probability of certain events occurring when two dice are thrown simultaneously. We hope that this article has provided you with a better understanding of the topic.
- What is the probability of getting a sum of 7 when two dice are thrown?
- What is the probability of getting a total number greater than 10 when two dice are thrown?
- What is the probability of getting a sum of 11 when two dice are thrown?
- What is the probability of getting a total number less than 5 when two dice are thrown?
- What is the probability of getting a sum of 12 when two dice are thrown?
- P(Sum = 7) = 1/6
- P(Total Number > 10) = 1/12
- P(Sum = 11) = 1/18
- P(Total Number < 5) = 1/6
- P(Sum = 12) = 1/36