When two dice are thrown, there are 36 possible outcomes (6 sides on the first die multiplied by 6 sides on the second die). Out of these 36 outcomes, 30 have different numbers on each die (since there are 5 different numbers on the second die for each number on the first die). Therefore, the probability that the numbers on the two dice are different is 30/36 or 5/6.
When two dice are thrown, the probability that their numbers are different can be calculated by considering the number of favorable outcomes (where the numbers on the dice are different) divided by the total number of possible outcomes.
There are 36 possible outcomes when two dice are thrown, as there are 6 sides on the first die and 6 sides on the second die. Each side on the first die can be paired with any of the 6 sides on the second die, resulting in 6 x 6 = 36 total outcomes.
Out of these 36 possible outcomes, we need to determine the number of outcomes in which the numbers on the two dice are different. To do this, we can think of it as selecting a number on the first die (which can be any of 1, 2, 3, 4, 5, or 6) and then selecting a different number on the second die (which can be any of the remaining 5 numbers).
The number of outcomes where the numbers on the two dice are different is 6 choices for the first die multiplied by 5 choices for the second die, giving us a total of 6 x 5 = 30 favorable outcomes.
Therefore, the probability that the numbers on the two dice are different is given by 30 favorable outcomes divided by the 36 total possible outcomes, which can be written as 30/36 or simplified to 5/6.
To make the text more interesting and informative, let’s add a quote from Albert Einstein – one of the greatest physicists and thinkers of all time:
“In the middle of difficulty lies opportunity.” – Albert Einstein
Interesting Facts about Dice and Probability:
- Dice have been used for games and divination purposes for thousands of years. Some of the earliest dice were found in ancient Mesopotamia (modern-day Iraq) dating back to around 3000 BC.
- A standard die (singular of dice) is a small, often cubical object with each of its faces marked with a different number of dots, called pips. The most common type of die is the six-sided die, also known as a D6.
- The probability of rolling a particular number on a fair six-sided die is 1/6, as there are 6 equally likely outcomes (1, 2, 3, 4, 5, or 6) and only one favorable outcome for each number.
- The probability of getting a sum of 7 when two fair six-sided dice are rolled is the highest. This is because there are six possible combinations that result in a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). The probability of rolling a sum of 7 is 6/36 or simplified to 1/6.
- Probability is a branch of mathematics that deals with the study of uncertainty and likelihood. It has widespread applications in various fields, including statistics, gambling, and decision-making.
Table:
| First Die | Second Die | Different Numbers? |
|---|---|---|
| 1 | 1 | No |
| 1 | 2 | Yes |
| 1 | 3 | Yes |
| 1 | 4 | Yes |
| 1 | 5 | Yes |
| 1 | 6 | Yes |
| 2 | 1 | Yes |
| 2 | 2 | No |
| 2 | 3 | Yes |
| 2 | 4 | Yes |
| 2 | 5 | Yes |
| 2 | 6 | Yes |
| 3 | 1 | Yes |
| 3 | 2 | Yes |
| 3 | 3 | No |
| 3 | 4 | Yes |
| 3 | 5 | Yes |
| 3 | 6 | Yes |
| 4 | 1 | Yes |
| 4 | 2 | Yes |
| 4 | 3 | Yes |
| 4 | 4 | No |
| 4 | 5 | Yes |
| 4 | 6 | Yes |
| 5 | 1 | Yes |
| 5 | 2 | Yes |
| 5 | 3 | Yes |
| 5 | 4 | Yes |
| 5 | 5 | No |
| 5 | 6 | Yes |
| 6 | 1 | Yes |
| 6 | 2 | Yes |
| 6 | 3 | Yes |
| 6 | 4 | Yes |
| 6 | 5 | Yes |
| 6 | 6 | No |
Some additional responses to your inquiry
5/6Given, two dice are thrown at the same time. We have to find the probability of getting a different number on both dice. Therefore, the probability of getting a different number is 5/6.
See a video about 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.
I’m sure you will be interested
Also, When two dice are thrown what is the probability that the difference of the numbers is 2? We have to determine the probability that the difference of the numbers on the two dice is 2. Therefore, the probability of getting the difference of the numbers on the dice as 2 is 2/9.
One may also ask, When two dice are thrown what is the probability of getting same number?
The reply will be: 1/6
When two dice are rolled what is the probability of getting same number on both? Sample points of getting same number on both dice- (1,1) ,(2,2) ,(3,3) ,(4,4) ,(5,5) & (6,6). Hence, the probability of getting same number on both the dice is 1/6.
Beside above, What is the probability of getting different odd numbers when two dice are thrown simultaneously? Calculation: When two dice are thrown. To get the two numbers whose product is odd, both should be odd numbers. ∴ The probability of getting two numbers whose product is odd is 1/4.
What is the probability of getting 7 when rolling 2 dice? Response will be: For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.
Hereof, What if two different dice are thrown together? Answer will be: Two different… Two different dice are thrown together. Find the probability that (i) the sum of the numbers appeared is less than 7. (ii) the product of the numbers appeared is less than 18. If two different dice are thrown together, they have numbers 1, 2, 3, 4, 5 and 6 and 1, 2, 3, 4, 5 and 6 on them.
How do you calculate the probability of 2 dice? The response is: For two dice, you should multiply the number of possible outcomes together to get 6 × 6 = 36. With subsequent dice, simply multiply the result by 6. If you use dice of a different shape, enter the number of their sides instead of 6. When rolling 2 dice, what is the probability of 7?
Simply so, How many permutations are there when 2 dice are thrown? When 2 dice are thrown, there are 36 possible permutations (different outcomes) of the two dice. If the first die lands on 1, 2, 5 or 6 – then in each case there is exactly one outcome on the second die that would result in a difference of two fro… Something went wrong. Wait a moment and try again.
Then, How many possible outcomes from rolling two dice? 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. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6.
What is the probability if 2 dice are thrown at the same time?
Answer to this: When 2 dice are thrown at the same time, the overall possible outcomes are Probability = number of favourable outcomes / number of possible outcomes Therefore, the probability of getting a different number is 5/6. ✦ Try This: Three dice are thrown at the same time. Find the probability of getting the same number on all dice.
Also asked, How do you distinguish between two dice?
Answer will be: When rolling two dice, distinguish between them in some way: a first one and second one, a left and a right, a red and a green, etc. Let (a,b) denote a possible outcome of rolling the two die, with a the number on the top of the first die and b the number on the top of the second die.
In this way, How do you determine the probability of a dice roll?
As a response to this: 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. For example, when only one die is rolled, as in the example above, the sample space is equal to all of the values on the die, or the set (1, 2, 3, 4, 5, 6).
Keeping this in view, How many possible outcomes from rolling two dice? The answer is: 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. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6.