For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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1answer
70 views

Creating unusual probabilities with a single dice, using the minimal number of expected rolls

Problem I want to create an 'event' with probability of $\frac{1}{7}$ with a single dice as efficiently as possible (to roll the dice as little as possible). To give you some better understanding of ...
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2answers
4k views

Variance and Standard Deviation of multiple dice rolls

I'm trying to determine what the variance of rolling $5$ pairs of two dice are when the sums of all $5$ pairs are added up (i.e. ranging from $10$ to $60$). My first question is, when I calculate the ...
2
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0answers
41 views

How to physically model/construct a biased coin?

A perfectly unbiased coin is one that has the same probability for heads and tails (i.e., 50%/50%). A perfectly biased coin is one that has (as the name suggests) different probabilities for head ...
2
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1answer
37 views

Given two dice, what's the probability that land on the last spot on the board?

So me and my colleagues are discussing board games and we land on the subject of the Danish "Matador" (Monopoly) and on that board there are 40 spaces. You start on Space 1 and are given two dice to ...
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2answers
106 views

Probability to obtain more than X with 3 dice.

This is a dice problem 1) I want to calculate the probability to have more than X throwing 3 dice of 6 faces. X = addition of the result of the 3 dice. 2) This is the first step but if you can also ...
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2answers
66 views

What's the probability of getting $5$ different numbers but not any $6$ when throwing $5$ dice?

I have $5$ dice, I throw them at once. What is the probability of getting $5$ unique numbers, i.e., $1\ \ \&\ \ 2\ \ \&\ \ 3\ \ \&\ \ 4\ \ \&\ \ 5$ in any order BUT NOT any $6$?...
0
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1answer
60 views

die game where we roll until we get a 5 or a 6

We roll a die until we get a $5$ and a $6$ for the first time, not necessarily consecutively and not necessarily in that order. We need to pay $x$ dollars before each die throw, and once both a $5$ ...
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2answers
1k views

What is the most unfair set of three nontransitive dice?

In a set nontransitive dice, each die is superior to another die, but is inferior to a third. It is similar to the game of rock-paper-scissors. Here is one example: ...
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4answers
809 views

Expected outcome for repeated dice rolls with dice fixing

Here is another dice roll question. The rules You start with n dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not ...
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4answers
66 views

Probability of a die rolled three times yielding three even numbers

A die is rolled three times. What is the probability of obtaining three even numbers ? I've solved this problem calculating the number of total results: $$u=D'_{6,3}=6^3$$ and the number of ...
2
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1answer
34 views

Finding probability that 2 has appeared atleast once given sum is 10 and die is thrown thrice?

An unbiased die is thrown three times; the sum of numbers coming up is 10. The probability that two has appeared at least once is: A 1/36 B 5/36 C 91/216 D 1/18 ? I was able to find out of 216 ...
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3answers
51 views

Probability of dice rolls

Two regular cubic dice are rolled. One is red and the other blue. What s the probability that the red die roll is greater that or equal to the blue die?
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1answer
737 views

Probability of dice roll (board games)

Assume that we have $n$ six-side dices. We will roll all the $n$ dices.What is a probability of getting at least $r$ ones, $s$ twos , $t$ threes and $u$ fours? Number $6$ can be used instead of any ...
1
vote
1answer
39 views

Throwing dice and finding limits

We throw an fair dice $n$ times. Let $S_n$ be the number of throws with even number of dots on the dice. 1.) Calculate the limit $$\lim_{n\rightarrow\infty}P(2S_n \leq n)$$ 2.) Express the value of ...
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2answers
26 views

Estimating a random variable from repeated trials

I have an $n$ sided die and suspect that it is biased. I'm interested in the probability of rolling a $1$, so I roll the die $m$ times and count up the number of times I roll $1$, then divide the ...
0
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1answer
38 views

Probability: Application Of “Expected Value”

$\newcommand{\P}{\mathbb{P}}$$\newcommand{\E}{\mathbb{E}}$So, I was learning expected value today and I'm trying to understand the significance of calculating this term "Expected value". In this ...
3
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1answer
27 views

Figuring out probability of dice with least amount of questions

Given $n$ dice, each with $k$ faces numbered $1,\dots,k$, you're allowed to ask me what the probability of some event happening is (a subset of all the possibilities and I give a number). What ...
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1answer
27 views

Probability of Getting a Yahtzee of Fives Given Two Fives

(The following problem is from MAML, Meet 3, Round 1, December 2012, Problem 3.) In the game of Yahtzee one has a chance to get Yahtzee (5 of the same kind, such as 5 sixes) in the throw of 5 ...
0
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1answer
45 views

What is the average and variation of $20$ dices?

If I roll a dice the average is $E(X) = (1+2+3+4+5+6)/6 = 7/2$ and $$E(X^2) = (1+4+9+16+25+36)/6 = 91/6$$ $$VAR(x) = E(X^2) - (E(X))^2 = 91/6 - 49/4 = 35/12$$ Now the question is: How I can find ...
0
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0answers
32 views

Confidence interval when rolling a dice

If you roll a die 20,000 times and from these rolls you get either a 1,2, or 3 11,000 times, how can you calculate the confidence interval at 95% for the probability to get a 1,2, or 3? The ...
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4answers
1k views

How many different dice exist? That is, how many ways can you make distinct dice that cannot be rotated to show they are the same?

Dice are cubes with pips (small dots) on their sides, representing numbers 1 through 6. Two dice are considered the same if they can be rotated and placed in such a way that they present matching ...
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2answers
475 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
1
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1answer
54 views

Dice rolls - Combinatorics with limitations

Given 2 players, one rolling $x$ d6 dice and the other rolling $y$ d6 dice, what is the probability of a match between the two players? I'm getting stuck on the sub-set comparisons - I can calculate ...
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3answers
35 views

“In tossing four fair dice, what is the probability of at least one three?” using complement

There is a very similar question here, and in both that question and this question I'm asking right now, the accepted answer involves using a complement. The same thing occurs in this textbook ...
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3answers
857 views

Probability sum of 5 before sum of 7

Pair of fair die are rolled (independently I hope) infinitely. Find probability sum of 5 appears before sum of 7. 2 approaches: $$P(\text{sum of 5 appears before sum of 7})$$ $$= P(\text{roll 1 ...
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votes
2answers
80 views

Find $\mathbb P (X_1 + \cdots + X_n = 6n-3)$

A fair die is tossed n times (for large n). Assume tosses are independent. What is the probability that the sum of the face showing is $6n-3$? Is there a way to do this without random variables ...
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0answers
21 views

Probability of getting a “full house” by rolling dice [duplicate]

In poker, full house means getting three cards with the same rank, and another two cards with the same rank (not the same as other three cards). I can understand how to use combination to solve this ...
0
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0answers
28 views

Calculating Probability Of Value With Dice [duplicate]

I am trying to write a program to calculate the probability of a number of dice thrown equaling a specif value. I have done some working out in excel, to try and find a patter, but I am at a loss. At ...
44
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2answers
33k views

Expected time to roll all 1 through 6 on a die

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die? The order in which the numbers appear does not matter. I had this questions explained ...
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3answers
4k views

Expected sum if a fair die is rolled continuously [closed]

The problem statement is : What sum can I expect in rolling a fair die n times? How to determine the mean in a convenient way? Consider the fair die is 6 sided
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2answers
34 views

Throwing x dice, chance of getting sum of at least y [duplicate]

I found some answers to this question, but that was with only two dice, with 6 sides. What if I have 30 dice, with 10 sides each (from 1 to 10). I can't make a matrix and count as was suggested on the ...
2
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1answer
39 views

Quick probability question on rolling 2 Die

If I flip a coin and it lands on heads I roll a fair dice n times. If the coin lands on tails I roll a biased dice n times. Let $X_i$ denote the score of the $i$th roll of the fair die and $Y_i$ the ...
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0answers
16 views

12 six-sided dice are thrown, what is the probability of getting each number at least once? [duplicate]

I got a bit confused and couldn't find the correct answer to check mine. This was the closest I could get: $\frac{6^6 \frac{12!}{6!6!}}{6^{12}}=\frac{924}{6^6}=0,0198$ where you have $12 \choose6$=$...
2
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1answer
51 views

Probability Mass Function of infinitely re-rolled dice

I play a game called Shadowrun. It is a role-playing game that uses a dice pool mechanic. A player has a dice pool of $x$ six-sided, unbiased dice. Every 5 or 6 counts as a success. The more successes,...
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2answers
54 views

The probability of rolling 4 dice and getting a 6.

The probability of rolling 2 dice and getting a 6 on either one of the die or both is : 11/36 or about 0.305. Also I calculate the probability of rolling 4 dice and getting a 6 on either one, two, ...
0
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2answers
29 views

Dice role: What is the probability to observe 2 times 1 and 2 times 5 with the outcome of a fifth die role being unknown?

I tried to solve the following exercise: Given a dice with $P(X=2) = P(X=4) = P(X=5) = \frac{2}{15}$ and $P(X=1) = P(X=6) = P(X=3) = \frac{2}{10}$. What is the probability to observe 2 times 1 and 2 ...
1
vote
1answer
19 views

Probability of rolling a five and a prime pair of six sided dice

This is a silly question, but I can't quite put my finger on where my reasoning is wrong. Given a pair of 6 sided dice, what is the probability of rolling a 5 and a prime? My answer: 6/36 Correct ...
6
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0answers
88 views

Progressive Dice Game

You have a fair, regular 6-sided dice. The game is played for $n$ turns. Each turn you make a roll and gain that many points the rolled side is showing, then do one of the following: ...
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0answers
69 views

Generalization of classic 3 roll die game to $n$ rolls

I am trying to generalize the following well-known 3 roll die problem: "We roll a single die no more than 3 times. We can stop immediately after the first roll, immediately after the second roll, or ...
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vote
3answers
125 views

Probability distribution of number of times required to roll all of a certain set of k numbers?

Consider a 12-sided fair die. What is the distribution of the number T of rolls required to roll a 1, a 2, a 3, and a 4? Taking inspiration from the Coupon Collector's Problem, I believe that the ...
0
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1answer
31 views

Any way to calculate chances of getting “n” hits when rolling “x” die (hit is when I roll more than “y”)?

First, let me preface - I saw similar questions already, but to be honest, I didn't understand the answers, or couldn't understand how to convert the answer for given question to my problem. My ...
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4answers
15k views

On average, how many times must I roll a dice until I get a $6$?

On average, how many times must I roll a dice until I get a $6$? I got this question from a book called Fifty Challenging Problems in Probability. The answer is $6$, and I understand the solution ...
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0answers
24 views

Probability of the n-th dice matching in 2 groups of sorted random numbers

Say we have 2 groups of 6 6-sided dice. Each group of dice is rolled and then sorted so we have 2 groups of sorted numbers. What is the probability of each die in the group matching the corresponding ...
3
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1answer
46 views

Two regular dice are rolled. Given that one of them is a $6$, what is the probability that the other is also a $6$?

I'm having trouble with the following question for and I have an exam in two days: Two regular dice are rolled. Given that one of them is a $6$, what is the probability that the other is also a $6$...
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6answers
392 views

Die that never rolls the same number consecutively

Suppose we have a "magic" die $[1-6]$ that never rolls the same number consecutively. That means you will never find the same number repeated in a row. Now let's suppose that we roll this die $1000$ ...
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2answers
69 views

Proof: Probability of a pair when rolling 7 dice is 1.

I know that the probability should be over or exactly 1 since out 6 possible values the 7th dice will always be a duplicate. My calculations are wrong though: $\frac{{7\choose2} 5! 6*1}{6^7}$ Why?...
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3answers
9k views

Probability of All Distinct Faces When Six Dice Are Rolled

If six fair dice are rolled what is probability that each of the six numbers will appear exactly once?
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2answers
47 views

Probability of disjoint dice results

You have $n = n_A + n_B$ $k$-sided dice. The $n_A$ dice are thrown and a set of the resulting values, call it $S_A$, is built; likewise for the $n_B$ dice, calling the resulting set $S_B$. What is ...
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4answers
11k views

How many rolls do I need to determine if my dice are fair?

Roughly how many times do I need to roll a 6-sided die to feel confident that it's giving "fair" results? What about a 10-sided or 20-sided die? Note that I will be actually manually rolling physical ...
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8answers
2k views

Probability that the sum of 6 dice rolls is even

Question: 6 unbiased dice are tossed together. What is the probability that the sum of all the dice is an even number? I think the answer would be 50%, purely by intuition. However, not sure if ...