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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2answers
19 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 ...
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1answer
29 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
23 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 ...
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1answer
39 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 ...
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0answers
30 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
467 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
52 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
31 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
848 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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2answers
79 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
27 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 ...
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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
32 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 ...
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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 ...
0
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0answers
15 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 $12 \choose6$=$...
1
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1answer
75 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 ...
0
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1answer
726 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 ...
2
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1answer
48 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,...
4
votes
2answers
52 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
28 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 ...
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1answer
18 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
82 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
67 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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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
26 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
14k 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 ...
0
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0answers
23 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
44 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 $6$...
23
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4answers
651 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 ...
10
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6answers
390 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 $1000$ ...
0
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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
46 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 ...
16
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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 ...
2
votes
1answer
40 views

What is the probability that the sum of two dice rolls is a multiple of $3$?

What is the probability that the sum of $2$ dice rolls is a multiple of $3$? What about for $3$ dice rolls? For $n$ dice rolls? So I have the first part of this solution worked out by writing out all ...
0
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1answer
59 views

Optimal bet according to the probability of win

Suppose the following game: You start with $5000; You will roll a dice 100 times; You have to choose a percentage of your accumulated money to bet all the 100 times. You will choose it only once and ...
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0answers
54 views

Dice throwing probability : at least one success

What would be the function for calculating the probability of at least one success of $n$ $10$-sided dice thrown, if success is $9$ or $10$, but $1$ is counted as negative success (or failure). In ...
14
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4answers
904 views

On the probability of getting the same number for three dice

I found the probability of having the same number when throwing 3 dice to be $1\times\left(\frac16\right)^2$. In addition, I don't understand how do people get the equation $\left(\frac16\right)^3\...
4
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1answer
51 views

Special dice generating non-decreasing sequence

Suppose that, when rolled for the first time, a special 6-sided dice shows $1,\ldots, 6$ with probability $\frac{1}{6}$ each, and then, upon rerolling, shows with equal probability a number greater or ...
4
votes
2answers
71 views

Probability of winning dice roll-off with a re-roll

I am looking to find the probability of winning a basic dice roll-off using a 6 sided die if one of the players can re-roll their die. The main thing that is throwing me off is that player 2 can re-...
0
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1answer
39 views

Calculating probability that 5 dice rolls will produce an average of 3.5

We are carrying out a dice game which involves 5 people rolling dice and passing buttons equal to the number rolled . We have to work out the probability that we will get an average of 3 .5 items ...
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2answers
58 views

Dice probability, Heaven or Hell [closed]

You're at the gate of Heaven and St. Peter asks you to play Dice with him. If you roll a 5 or 6, he'll let you into Heaven. However, if you roll a 2,3 or 4, you'll be sent to hell. If you roll a 1, he ...
0
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2answers
38 views

Find dependent event when two dice are thrown simultaneously.

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of ...
2
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0answers
36 views

Can someone help me balance this game (probability question) [closed]

A team of 9 vs a team of 1. Each round each of "the 9" roll a die to "attack" and "the 1" rolls 9 dice to "defend", the nine dice are preassigned to attackers before the roll, "the 1" cannot choose ...
0
votes
1answer
33 views

Given three six-sided dice, what is the probability that the value of the third will be greater than the sum of those of the first two?

A die is rolled three times, or three dice are rolled. What is the probability that the third die values greater than the sum of the first two? (assuming six-sided dice, but I would be interested in ...