Probability:
The 6 Sided Dice Probability Calculator helps you determine the likelihood of rolling specific sums when using multiple 6-sided dice. Whether you're playing a board game, conducting a probability experiment, or simply curious about dice outcomes, this calculator provides quick and accurate probability calculations. By inputting the number of dice and the desired sum, you can easily find out how likely it is to roll that sum.
Formula of 6 Sided Dice Probability Calculator
When rolling more than one 6-sided die, the calculation of probabilities involves considering the combined outcomes. Here’s how to calculate probabilities for multiple 6-sided dice.
Rolling Two 6-Sided Dice
When rolling two 6-sided dice, each die has 6 faces. The total number of possible outcomes is the product of the number of outcomes for each die.
Total number of possible outcomes = 6 * 6 = 36
Probability of Rolling a Specific Sum
To calculate the probability of rolling a specific sum, you need to determine the number of favorable outcomes that produce that sum.
For example, to find the probability of rolling a sum of 7 with two dice, the possible combinations are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
Number of favorable outcomes = 6
Probability of rolling a sum of 7 = Number of favorable outcomes / Total number of possible outcomes Probability = 6 / 36 = 1 / 6
Rolling Three 6-Sided Dice
When rolling three 6-sided dice, the total number of possible outcomes is: Total number of possible outcomes = 6 * 6 * 6 = 216
Probability of Rolling a Specific Sum
To calculate the probability of rolling a specific sum with three dice, you need to determine the number of favorable outcomes.
For example, to find the probability of rolling a sum of 10 with three dice, some possible combinations are:
- (1, 3, 6)
- (1, 4, 5)
- (2, 2, 6)
- (2, 3, 5)
- (2, 4, 4)
- (3, 3, 4)
The exact number of favorable outcomes can be complex to calculate manually.
Probability of rolling a specific sum = Number of favorable outcomes / Total number of possible outcomes
General Formula for Multiple Dice
For n dice, each with 6 sides: Total number of possible outcomes = 6^n
Probability of a specific outcome: Probability = Number of favorable outcomes / 6^n
Pre-calculated Probability Table
Here is a table with common probabilities for quick reference:
| Number of Dice | Sum | Probability |
|---|---|---|
| 2 | 7 | 1/6 |
| 2 | 11 | 2/36 |
| 3 | 10 | 27/216 |
| 3 | 18 | 1/216 |
Example of 6 Sided Dice Probability Calculator
Let's walk through an example using the calculator. Suppose you want to find the probability of rolling a sum of 9 with three 6-sided dice.
- Determine the total number of possible outcomes: Total outcomes = 6 * 6 * 6 = 216
- Identify the favorable outcomes: Possible combinations:
- (1, 3, 5)
- (1, 4, 4)
- (2, 2, 5)
- (2, 3, 4)
- (3, 3, 3)
- Count the number of favorable outcomes: Number of favorable outcomes = 5
- Calculate the probability: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 5 / 216
Most Common FAQs
The calculator uses the total number of possible outcomes and the number of favorable outcomes to determine the probability of rolling a specific sum with multiple dice.
Yes, the calculator can be used for any number of dice. The general formula for multiple dice helps you calculate probabilities regardless of the number of dice.
This calculator is useful for board games, educational purposes, probability experiments, and any scenario where you need to understand the likelihood of specific dice outcomes.