Dice Probability Calculator is a free online tool to describe the probability of dice roll over numerous variants. Simply, you just need to provide the respective inputs and hit the calculate button and get the answer in a fraction of seconds.
How do you Calculate the Probability of a Dice ?
Before finding the probability of a dice we need to make sure that for what kind of dice we are going to find the probability.
Probability of Rolling Same Value on each Die: Chance of obtaining a particular value on a die is p, simply we need to multiply the probability by itself as many times the number of dice. In other words, we can put it as P = pn
Probability of Rolling all Values Equal or Higher than y: This scenario is near to the above one but the difference is this time p is 1/s multiplied by all the possible conditions fulfilling the first condition.
Probability of Rolling all Values Equal or Lower than y: This case is also similar to the earlier one but it's just that here we are finding the numbers which are equal or lower than our target.
The probability of rolling exactly X same values (equal to y) out of the set: This case is a bit different from the earlier ones. But Binomial Probability comes in handy here. The formula for describing the binomial probability is P(X=r) = nCr * pʳ * (1-p)ⁿ⁻ʳ where r is the number of successes, nCr is the number of combinations.
The probability of rolling at least X same values (equal to y) out of the set: In this particular scenario the probability is the sum of probabilities.
The probability of rolling an exact sum 'r' out of the set of 'n' s-sided dice: The general formula is quite complex.
The probability of rolling a sum out of the set, not lower than X: Similar to the earlier cases we need to determine the results that match the initial condition and then divide them with a number of all possibilities.
Probability of rolling a sum out of the entire set, not higher than X: Most of the process is same but in this we need to add only the sums below or equal to the target. To find the sum of all the sums can take up huge time so you can go with the complimentary events as total probability sums to 1 you can simply subtract from 1.
Here, in these, we have some variables that are used in these variables.
- n is the number of dice
- s is the number of individual die faces
- p is the probability of rolling any value from a die
- P is the overall probability
There is an easy relationship - p = 1/s
Steps to Find the Dice Probability ?
Follow the below steps or guidelines to calculate the probability of dice easily and quickly.
- Firstly, you need to write the given values in the problem.
- Then apply the probability formula of a die.
- Substitute the values in it and simplify.
- Finally, you will get the desired answer.
Dice Probability Example Questions
Question 1: When a die is rolled. Find the probability of getting an even number?
Formula, probability = No. of favorable outcomes / Total No. of possible outcomes
Favorable outcomes for getting an odd number when a dice is rolled is(2, 4, 6) 3
Total number of possible outcomes = 6
Substituting values we have the probability of getting an even number = 3/6
Probability of getting an odd number = 1/2
Therefore, the probability of getting an even number when a dice is rolled is 1/2.
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FAQs on Combinations Calculator
1. What is the formula to find the probability of a die?
The formula to calculate the probability is, probability = No. of favorable outcomes / Total No. of possible outcomes
2. How to use the Dice Probability Calculator?
- Enter the values in the input fields.
- Then, click the calculate button.
- And get the output straight away
3. What is the probability of rolling a 7 with two dice?
Here, No. of Favorable outcomes is = 6
The Total no. of outcomes when two dice are rolled is 36
probability = No. of favorable outcomes / Total No. of possible outcomes = 6/36 = 1/6.