Table of Contents
What is the probability of rolling a sum of 5?
The probability of rolling a pair of dice whose numbers add to 5 is 4/36 = 1/9.
How do you find the standard deviation of a roll of dice?
The standard deviation is the square root of 35/12 = 1.7078… (the value given in the question.) If one die has a mean of 3.5 and a variance of 35/12, then thirty dice have a mean of (30)(3.5) = 105 with a variance of (30)(35/12) = 87.50. The standard deviation is √87.50 = 9.354+.
What is the probability of rolling a 5 on a 6-sided dice?
Two (6-sided) dice roll probability table
| Roll a… | Probability |
|---|---|
| 5 | 10/36 (27.778\%) |
| 6 | 15/36 (41.667\%) |
| 7 | 21/36 (58.333\%) |
| 8 | 26/36 (72.222\%) |
What is the probability that you will roll a sum of six?
5/36
Answer: The probability of rolling a sum of 6 with two dice is 5/36.
What is the variance of a six sided dice?
When you roll a single six-sided die, the outcomes have mean 3.5 and variance 35/12, and so the corresponding mean and variance for rolling 5 dice is 5 times greater.
What is a fair dice?
At its simplest, a fair die means that each of the faces has the same probability of landing facing up. A standard six-sided die, for example, can be considered “fair” if each of the faces has a probability of 1/6.
What is the expected value of a 6 sided dice?
The expected value of a dice roll is 3.5 for a standard 6-sided die. This assumes a fair die – that is, there is a 1/6 probability of each outcome 1, 2, 3, 4, 5, and 6. The expected value of the sum of two 6-sided dice rolls is 7. Dice with a different number of sides will have other expected values.
What is the expected value of 3 dice rolls?
The expected value of 3 dice rolls is 10.5 (assuming we take the sum of the three dice rolls). When we roll 3 6-sided dice and sum the results (or roll one die three times and sum the results), we get a larger expected value than if we just rolled one or two dice.
What is the distribution of X on a fair six-sided die?
Let x be the number showing on a fair six-sided die. The distribution of x has a mean of 3.5 and a standard deviation of 1.71. If a six-sided die is rolled 30 times, what is the probability that the average of all 30 rolls is less than 3?
What is the probability of rolling a 12 sided die?
The expected value of a dice roll is 6.5 for a standard 12-sided die (a die with each of the numbers 1 through 12 appearing on exactly one face of the die). In this case, for a fair die with 12 sides, the probability of each outcome is the same: 1/12. The possible outcomes are the numbers 1 through 12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.