The probability of getting a sum of 1 or 7 when rolling two dice once is 1/6. There are 6 possible outcomes when rolling two dice, and only one of those outcomes results in a sum of 1 or 7 (rolling a 1 on one die and a 6 on the other, or rolling a 6 on one die and a 1 on the other).
When two dice are rolled, there are various possible outcomes that can occur. However, we are specifically interested in the probability of obtaining a sum of 1 or 7 when both dice are rolled once.
The probability of getting a sum of 1 or 7 can be calculated by finding the number of favorable outcomes (outcomes that meet the desired condition) and dividing it by the total number of possible outcomes. Let’s analyze this situation in more detail.
To obtain a sum of 1, only one combination is possible: rolling a 1 on one die and a 1 on the other die. On the other hand, to obtain a sum of 7, there are two favorable combinations: rolling a 1 on one die and a 6 on the other, or rolling a 6 on one die and a 1 on the other.
Now, let’s construct a table to further illustrate the possible outcomes and their probabilities:
| 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 |
From the table, we can see that there are two favorable outcomes to obtain a sum of 1 or 7. Out of the total 36 possible outcomes (6 faces on the first die multiplied by 6 faces on the second die), the probability is 2/36 or 1/18.
To further enhance the understanding of probability, Albert Einstein once said, “The only way to comprehend mathematics is to do mathematics.” This insightful quote reminds us that by actively engaging with mathematical problems, we can deepen our understanding and grasp abstract concepts more effectively.
Interesting facts about dice and probability:
- Dice are one of the oldest known gambling tools, with origins dating back over 5,000 years.
- Traditional dice are cubical in shape, with each face displaying a different number of dots, often called pips.
- The sum of numbers on opposite faces of a die always equals 7. For example, if one face displays a 6, the opposite face will show a 1.
- The probability of rolling any specific number on a fair six-sided die (also known as a D6) is 1/6.
- When two dice are rolled, the total number of possible outcomes is 36 (6 possibilities for each die, resulting in 6 x 6 = 36 combinations).
- The probability of rolling a sum of 3, 4, 5, 6, 8, 9, 10, 11, or 12 when two dice are rolled once is higher than the probability of rolling a sum of 1 or 7.
Watch a video on the subject
The video explains the process of calculating the probability of rolling a seven with two dice. By considering the favorable and total cases, the speaker determines that there are six favorable combinations out of a total of 36 combinations. This results in a simplified probability of 1/6, meaning the chances of rolling a sum of seven with two dice are one out of six.
Identified other solutions on the web
There are 36 possible ways two dice can roll, so the probability of the sum of seven is 6 out of 36, or 1/6.
I’m sure you’ll be interested
Herein, What is the probability that the sum is 7 if you roll two dice once? 1/6
The probability of rolling two dice and getting a sum of 7 is 1/6.
Subsequently, What is the probability of getting a sum as 7 of the numbers on two dice when two different dice are thrown together? Response will be: ∴ The probability of getting sum as 7 when two dice are thrown is 1/6.
Also, How many ways can you get a sum of 7 in two dice?
The response is: When two dices are rolled, there are six possibilities of rolling a sum of 7 .
One may also ask, What is the probability of getting a 7 after rolling a single dice? Answer: 0
probability of occurrence of this event is zero. We know that, A die only has dots or numbers from 1 to 6, i.e., 1,2,3,4,5,6. ∴ The probability of getting number 7 = 0.
Also question is, What is the probability of rolling two dice and getting 7?
The response is: Let A = sum of numbers is 7 = { (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)} Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6. The probability of rolling two dice and getting a sum of 7 is 1/6.
Hereof, How many combinations of two dice give a sum of 7? The probability of each one of those is 1 36. How many possible combinations of two dice will give you a sum of 7? There are 6 combinations: (1,6), (6,1), (2,5), (5,2), (3,4) and (4,3). For a sum of 11, there are 2 combinations: (5,6) and (6,5). For a sum of 12, there is just 1 combinations: (6,6).
What is the probability of getting a sum of 7? What is the probability of getting a sum of 7 when two dice are thrown? So, pairs with sum 7 are (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1) i.e. total 6 pairs Probability of getting the sum of 7 = Favorable outcomes / Total outcomes So, P (sum of 7) = 1/6. Question 1: What is the probability of getting 1 on both dice? So, P (1,1) = 1/36.
What is the probability of rolling a 1 & 2? The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on. But what happens if we add another die? What are the probabilities for rolling two dice? To correctly determine the probability of a dice roll, we need to know two things: In probability, an event is a certain subset of the sample space.
What is the probability that the sum of two dice rolls is even? The response is: P ( ≡ 0 mod 6) 1 / 6 ( i 0 5 P ( previous sum was i 6)) 1 6 ( 1) 1 6. The sum of two dice rolls is even if both dice display even numbers or both display odd numbers. Hence, the probability that the sum of the two dice rolls is even is
In this way, What is the probability of getting a sum of 7? What is the probability of getting a sum of 7 when two dice are thrown? So, pairs with sum 7 are (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1) i.e. total 6 pairs Probability of getting the sum of 7 = Favorable outcomes / Total outcomes So, P (sum of 7) = 1/6. Question 1: What is the probability of getting 1 on both dice? So, P (1,1) = 1/36.
Additionally, How many combinations of two dice give a sum of 7? The probability of each one of those is 1 36. How many possible combinations of two dice will give you a sum of 7? There are 6 combinations: (1,6), (6,1), (2,5), (5,2), (3,4) and (4,3). For a sum of 11, there are 2 combinations: (5,6) and (6,5). For a sum of 12, there is just 1 combinations: (6,6).
Also Know, What happens if you roll two dice?
In reply to that: One roll has no effect on the other. When dealing with independent events we use the multiplication rule. The use of a tree diagram demonstrates that there are 6 x 6 = 36 possible outcomes from rolling two dice. Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6.