The probability of rolling three six-sided dice and getting a different number on each die is 6/120, which simplifies to 1/20. This is because there are 6 possible outcomes for the first die, 5 for the second, and 4 for the third, out of a total of 6^3 = 216 equally likely outcomes.
The probability of rolling three six-sided dice and getting a different number on each die can be calculated by analyzing the possible outcomes and dividing it by the total number of equally likely outcomes. This can be further explained with the help of interesting facts, a quote, and a table.
Explanation:
To determine the probability, we need to look at the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, the favorable outcome is rolling three different numbers on the three dice, and the total number of possible outcomes is the total number of equally likely outcomes when rolling three six-sided dice.
Let’s break it down step by step:
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Determine the favorable outcomes:
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The first die can land on any of the six numbers (1, 2, 3, 4, 5, or 6).
- For the second die, there are now only five remaining numbers to choose from.
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Similarly, the third die has four remaining numbers to choose from.
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Calculate the total number of outcomes:
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Each die has six possible numbers it can land on.
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Since there are three dice, the total number of outcomes is 6^3 = 216.
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Calculate the probability:
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The probability is the number of favorable outcomes divided by the total number of outcomes.
- In this case, there are 6 possible outcomes for the first die, 5 for the second, and 4 for the third. So, the probability is (6 * 5 * 4)/216 = 120/216 = 5/9.
Quote:
“A thorough understanding of probability is perhaps the strongest weapon in a statistician’s arsenal.” – Richard Routledge
Interesting facts about dice:
- The use of dice dates back over 5000 years, with the oldest known dice found in a 5000-year-old backgammon set in Iran.
- The standard six-sided dice, also known as a cube, is the most common type of dice used in games.
- The opposite sides of a six-sided die always add up to 7.
- Dice have been used for divination purposes, gambling, and decision-making throughout history.
Table:
| Die 1 | Die 2 | Die 3 |
|---|---|---|
| 1 | 2 | 3 |
| 1 | 2 | 4 |
| 1 | 2 | 5 |
| 1 | 2 | 6 |
| 1 | 3 | 2 |
| 6 | 5 | 4 |
In this table, each row represents a different outcome of rolling three six-sided dice, with each column representing the value rolled on a specific die. The table demonstrates the 120 different possible outcomes.
Overall, the probability of rolling three different numbers on three six-sided dice is 5/9. Understanding probability and its applications is essential in various fields such as statistics, gambling, and decision-making. As Richard Routledge suggests, a deep understanding of probability can be an invaluable tool.
Watch related video
Maria, a mathematician, provides a straightforward explanation of how to determine the probability of rolling a dice when the number is greater than 3 and less than 5. By considering all the possible outcomes (numbers 1 to 6) and noting that only the number 4 satisfies the condition, Maria concludes that the probability is 1 out of 6.
Other responses to your inquiry
1/6 of the time the first two dice will be same, and if not, there is a 1/3 that die #3 will match one of the first two dice: So we have 1/6 + (1/3 x 5/6) = 1/6 +5/18 = 4/9. 5/9 of the time all numbers will be different, and 4/9 of the time they will not.
The probability of rolling three six-sided dice and getting a different number on each die is 5/9. The total number of outcomes is 6x6x6 = 216. The number of favorable outcomes is 6c15c14c1 = 120. Therefore, the probability of getting a different number on each die is 120/216 = 5/9. Another way to calculate the probability is to use the formula $1cdot$$1over 6$$cdot {1over 6}$.
three dices were rolled total outcome 6x6x6 different number should appear on each favorable outcome= 6c1*5c1*4c1 probability= favorable/total ans= (6*5*4)/ (6*6*6)= 5/9
Well, the probability would be $1cdot$$1over 6$$cdot {1over 6}$ because for three dice, there are six outcomes for the same number because there are six numbers, so put in a 1 for the first factor and every other outcome will be different numbers and you’re talking about six-sided dice, so use $1over 6$s for the next two factors.
More interesting questions on the issue
What is the probability of rolling 3 dice and getting different numbers?
Answer: If three dice are tossed, then the probability that the numbers shown will all be different is 5/9.
What’s the probability of rolling 3 on a six-sided die?
As an answer to this: one-sixth
There is only one three on the die, so there is only one successful outcome. So, by dividing the number of successful outcomes by the total number of outcomes, we find that the probability of rolling a three on a regular six-sided die is one-sixth.
What is the probability of rolling an odd number on a die?
The probability when rolling a regular six-sided dice that the score is an odd number is three-sixths or three out of six. Both three and six are divisible by three. Therefore, this fraction could be simplified to one-half.
What are the possible combinations of three six-sided dice?
In reply to that: 216 outcomes
Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice. If we roll n dice then there are 6n outcomes.
Similar
What are all the possible outcomes of Rolling 3 dice?
The answer is: We multiply and see that there are 6 x 6 x 6 = 216 possible outcomes. As it gets cumbersome to write the repeated multiplication, we can use exponents to simplify work. For two dice, there are 6 2 possible outcomes. For three dice, there are 6 3 possible outcomes. In general, if we roll n dice, then there are a total of 6 n possible outcomes.
What is the probability of rolling a 3 on a six sided dice?
The response is: The chance of rolling a total of 2 is 2.78 percent The chance of rolling a total of 3 is 5.56 percent The chance of rolling a total of 4 is 8.33 percent
What are the odds of rolling dice?
Answer: The most likely outcomes when rolling three dice at once are 10 and 11. Each of these numbers has a 12.5% likelihood of being rolled. Both numbers each have 27 combinations that could result in 10 or 11. Because there are three dice instead of two, the number of possible combinations increases from 36 to 216.