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Questions tagged [dice]

For questions on dice, small throwable objects 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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Expected value of the sum of three different die

Suppose you have a 4-sided die, a 6-sided die, and a 12-sided die. You roll the three dice and add up the numbers that show up. What is the expected value of the sum of the rolls? My attempt solution ...
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1answer
49 views

A game with an $n$-sided die

Suppose you play a game with a fair $n$ sided die (that, if being rolled yields us a discrete random variable uniformly distributed on $\{k \in \mathbb{N}| k \leq n\}$). You play the following ...
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A Casino game called Winno consists of playing 10 bets. [closed]

A gambler wins a bet if he or she plays a "6" or a prime number from the outcome of a fair die. Each bet costs GHS10.00 and a win yields GHS15.00. However, if the gambler loses a bet, he pays ...
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How do I show that the MLE for all sides of a die is the same as MLE for 5/6 sides of a die

I have two sets of hypotheses: $H_0$: each of the six sides of a die has probability 1/6 of being rolled, versus $H_a$ being not $H_0$ $H_0$: 5 sides of a six-sided die each has probability 1/6 of ...
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Is a Spindown d20 still fair?

Is a Spindown d20 (numbers arranged consecutively around the instead of 21-sums arrangement) still fair to roll, given enough dice action to eliminate human variables, compared to a standard d20?
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1answer
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Roll n 3-sided dice (ABC). What's the probability of at least one A and two Bs?

Suppose you have n three-sided dice, with sides labelled A, B, C. What is the probability of getting ABB among your dice (i.e. at least one A, at least two Bs)? Order is not important. (By ...
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1answer
19 views

Probability that a die game ends on an even throw (Linear Solution)

I've researched solutions for this problem seeing as I couldn't seem to solve it on my own, and there's one in this very forum that albeit looking the most simple, I can't fully understand. Here is ...
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1answer
28 views

Chance of rolling highest after removing highest and lowest?

The problem: Say two people each roll 3 20-sided dice (a total of 6 dice). Person 1, only keeps the lowest die from the throw. Person 2, only keeps the highest die from the throw. What is the chance ...
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Risk free money using dice game

Given a six-sided fair dice. For each dice roll one receives the rolled number as return (in €, expectation: $3.5€$). For this exact game there are two available prices: $3.5€$ and $3.4€$. I am asked ...
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2answers
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Suppose we roll a die repeatedly and let Tk be the number of rolls until some number appears k times in a row.

Suppose we roll a die repeatedly and let Tk be the number of rolls until some number appears k times in a row. (a) Find P(T2 = k) for each integer k ≥ 2. (b) Find E[T2]. I am thinking that P(T2=2) = (...
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Algorithm to build a dice with given probabilities

Let's define a dice as a solid that, if rolled over a perfect horizontal plane, ends up being in a physically stable unambiguous state labelled $n$. The dice has $N$ states. Each state $n$ has a ...
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3answers
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Rolling multiple 10-sided dice or a single die + a modifier

If you have the option to roll 2 separate 10-sided dice or a single 10-sided die that you add 2 to the result with a goal of at least one die getting a specific number or higher (say 6 for the ...
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2answers
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probability of subset contained in dice rolls of custom dice with duplicate symbols

I play a game where you roll 24 dice, 6 of 4 different colors with each color having a different set of numbers and math operations these are the dice colors and possible symbols, there are 6 dice of ...
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1answer
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Probability of failing before a second condition

This question came up during a D&D game I was playing in and I found that I was unable to come up with an answer. I believe this should be a summation question, but I may be entirely off: You ...
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2answers
58 views

Probability throwing less than 16 with 12 dice

We've got 12 dice with the numbers 0,1,1,2,2,3 on it. What's the chance you throw 16 or less? I've trouble calculating it because of the different probabilities of throwing 0 ($\frac{1}{6}$) or ...
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0answers
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Finding the pmf of a r.v. S ~ Poisson's multinomial distribution. [duplicate]

Notation # categories $= c$. # trials $= t$. Side $i$ = $si$. Random vector $= S = \left[S_1\;S_2\;\ldots\;S_c\right]^T$. # occurrences of $si$ vector $= s = \left[s1\;s2\;\ldots\;sc\right]^T$. ...
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2answers
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Can a set of 6 sided die, simulate any other die? [duplicate]

So suppose I only have 6 sided dice, or D6. I want to play an RPG where a D20, or D10 is required. Can I simulate a D20 or D10 or any other sided die, using one or more D6?
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1answer
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Is this shape a fair D-24?

I've been looking at polyhedra, incuding Platonic solids as well as Archimedean and Catalan solids. Catalan solids are face-transitive, which I believe implies that they are "fair dice", in the sense ...
2
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1answer
70 views

Calculating the probability that the sum of the 2 highest values of n dice is equal to x

I'm trying to calculate the probability of the 2 highest values of n dice sum. In these calculations i'm currently assuming a 7-sided die that is thrown 3 times. With raw number i've found out ...
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2answers
333 views

Probability of rolling a pair of dice

Suppose we have two fair dice and rolled them. Let $A$ be the event "the sum of the two dice is equal to $3$"; $B$ be the event "the sum of the two dice is equal to $7$"; $C$ be the event "at least ...
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Expected value and Variance question

So let $A$ be the event the die falls either "one", "two", or "three" Let $B$ be the event the die falls either "four" or "five" and let $C$ be the event the die falls "six" $P(A) = \frac{1}{2}$, $...
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1answer
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How would I be able to use combinations or permutations to show double dice probability?

I am doing an experiment where I am comparing the probability of each of the numbers from $2$ to $12$ when using two dice. Getting the percentage for each number is easy enough, but now I want to show ...
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4answers
106 views

Number of attempts to see all faces $1, 2, 3, …, 6$ when rolling a dice? [closed]

Recently I have been thinking about the following random experiment: we repeatedly roll a dice until we see all the faces $1, 2, 3, 4, 5, 6$ of the dice at least once. Let $X$ = number of attempts ...
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1answer
28 views

If using a 3 sided dice, what is the probability of landing on a 1 exactly 3 times and on a 2 exactly two time?

If using a 3 sided dice and you roll the dice 7 times, what is the probability of landing on a 1 exactly 3 times and on a 2 exactly two times?
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2answers
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Two players throw a die until the sequence $1,2,3$ appears, and the winner is the one who roll $3$. What is the probability the second player wins?

Alameda and Belisario alternate turns throwing a fair die. Alameda plays first and they continue throwing, one at a time, until the sequence $1$-$2$-$3$ appears. Whoever throws the $3$ is the winner. ...
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0answers
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Probability of rolling fewer than m distinct numbers on n sided die after k rolls

Question Suppose I have an n-sided die which I roll k times. For any given m $\le$ n, what is the probability that I roll $\le$ m distinct numbers. Follow-up What is the smallest m such that I can ...
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1answer
55 views

Conditional Probability - A die is tossed 5 times.

A die is tossed 5 times. Given that the die falls six at least once, what's the probability it falls six at least twice? Let $A$ be the event the die falls six at least once. $P(A) = 1 - (\frac{5}{6})...
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3answers
57 views

Roll a a die three times

Draw probability mass function for the following random variables. I have tried $P(X=1)=(6/6)^3-(5/6)^3$ which gives me the minimum value rather than the maximum value. For $P(X=6)=1/6^3$.
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2answers
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Two dice: $\Pr(X_1 \lt X_2 \mid X_1 \leq X_2)$

This question comes from a completed, marked, and returned exam. It will not likely be reused. Problem The problem statement gives a fair die labeled 1-6. Let $X_1,X_2$ denote the two observed ...
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1answer
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Which is the correct way to determine the mean result of 1d12 reroll 1s & 2s?

I know the mean is simply the sum of the members divided by the number of them, so the average value given by rolling one $12$ sided die once is $(1+2+3...11+12)/12$ for $6.5$. Straightforward enough. ...
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2answers
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A die is rolled 5 times. How many outcomes will result in 5 different numbers? How many outcomes will have the 5th number equal to an earlier number?

A die is rolled $5$ times. How many outcomes will result in $5$ different numbers? How many outcomes will have the $5$th number equal to an earlier number? For the first part I did: $$6 \times 5 \...
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1answer
23 views

Probability space and independence [closed]

I am studying probability theory and one of the questions that I have faced is this. The problem is that I either don't know where to go about with this question or even if I do do something about it, ...
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2answers
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When does the game end?

A recent question has inspired the following one. $M$ people ($M\ge2$) play the following game. Each round every person admitted to the round rolls a $K$-sided dice ($K\ge2$), the sides being marked ...
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1answer
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Dice Rolls Between Three Players

The setup of the game involves three players and a fair, six-sided die. The rules are: If a player rolls a six, they win the game, if they roll an odd number, they pass the die to the player on their ...
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2answers
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Probability that no decision is reached in the first n trials

Three siblings cannot agree which TV programme to watch. They decide that each of them rolls a fair die and that the person with the highest number gets to choose the TV programme. If two or more ...
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Adding the sum of 6 Dice, how do you calculate the permutations?

By working out the different combinations for the sum being 6,7 and 8, (1, 6, and 21) I can see this is a diagonal row in pascals triangle but I can’t work out how these would be calculated without ...
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1answer
29 views

What is the probability that I actually won the game

Question I have two blue dice, with which I play a game. If I throw a double six (i.e. if I get two six on both the dices) then I win the game. I separately throw a red die. If I get a one, then I ...
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4answers
70 views

Discrete Probability: Four dice are thrown, what's the probability that…

Four dice are thrown, what's the probability that: a) None of them fall higher than three? b) None of them fall higher than four? c) That four is the highest number thrown? So for a, I wanna think ...
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2answers
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Fix $0\leq\delta\leq1.$ Bob rolls a die repeatedly in the hopes of rolling a six.

Fix a parameter $0\leq\delta\leq1.$ Bob rolls a die repeatedly in the hopes of rolling a six. However, after each failure to roll a six he gives up with probability $1-\delta$ and decides to try again ...
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2answers
41 views

Finding probability when two dice are rolled [closed]

You have two dice. Die one is a standard die with the six faces marked from 1 to 6. The second die has two faces marked with 1, two faces marked with 2 and two faces marked with 3. Both dice are ...
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3answers
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If a die is tossed 10 times and six of the tosses are 1s, what is the expected number of 2s in the 10 tosses?

If a dice is tossed $10$ times and six of the tosses are $1$s, What is the expected number of $2$s in the $10$ tosses? I don't know if I'm overthinking this or not. Do I need to include the $6$ ...
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1answer
57 views

Rolling 9 dice probability

Nine fair dice are rolled simultaneously. What is the probability of getting three pairs? My attempt: $$P(A) = \frac{\binom{6}{3}\binom{9}{2}\binom{7}{2}\binom{5}{2}\times3\times2\times1}{6^{9}}$$ ...
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2answers
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Two dice rolls, intersection of two events

Let's say we throw two dice and event $A$ is at least one die is 5, event $B$ is sum of two numbers is even. So we have a set of outcomes for: $A$ = $\{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(1,5),(2,...
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probability of dice rolls, the way to write set of outcomes

So, assume that we roll a die until 3 turns up. Let $A$ be the event that the first time a 3 turns up is after an even number of rolls which means odd throw. How do we find and write the set of ...
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1answer
42 views

Probability - What is the probability of obtaining a three of a kind or more when rolling six dice?

I understand that if you wanted to compute the probability of rolling a specific three of a kind or more (getting three or more $1$s for example) then you would just calculate $$\sum_{k=0}^3(5^k){6\...
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1answer
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What is the probability that when rolling five fair dice at least two show same number? [closed]

What is the probability that when rolling five dice at least two of the dice show the same number? Express your answer as a common fraction.
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2answers
52 views

Probability of winning 3+/4 rolls

I have a pretty basic probability question that's bugging me. Say we have two dice, a and b. When rolling both dice together, dice a has a $\frac{1}{5}$ chance of winning a roll round and dice b has ...
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1answer
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Rolling fair die twice and not getting doubles

I am taking intro stats. This is a practice problem from my book, and I am a little confused about whether to use conditional probability or if I am thinking about the problem incorrectly. If we roll ...
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1answer
51 views

A die is thrown until the first time the total sum of the face values of the die is 700 or greater. What is the probability for $n$ tosses?

Estimate the probability that, for this to happen, more than 210 tosses are required less than 190 tosses are required between 180 and 210 tosses, inclusive, are required We're supposed to be using ...
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3answers
90 views

Probability that the sum of three dice is not greater than 9

What is the probability that the sum of 3 indistinguishable dice is less than or equal to 9? I have tried counting the pairs $X_1, X_2$ such that their sum is less than or equal to 8, but I seem to ...