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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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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
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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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0answers
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Probability and random discrete variables: the PMF for the number of rolls it takes for a 6 sided die to repeat a number

We keep rolling the die as long as no value is repeated. When we see the first repeated value, that is the last roll. Let $X$ be the number of rolls it took. What is the PMF of X. Here's what I came ...
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1answer
38 views

Expected values, covariance [on hold]

Let's say I want to calculate the covariance of something, for instance the number that occurs on a first die compared to a second die rolled. Using the covariance formula we get: $Cov(X,Y) = E(XY)−E(...
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2answers
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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
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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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1answer
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Odds of rolling 10 dice with 2 having the same number [closed]

So I was actually thinking of a way how to solve this. I know the approach for finding the two dices probability which is pretty easy with $1/36$ however I am confused on how to execute it when there ...
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3answers
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Expectation of maximum value of three dice [closed]

Let $N$ be the maximum value of three dice. What is the expectation of $N$?
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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
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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
37 views

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
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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
33 views

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
49 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
55 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 ...
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2answers
289 views

PMF of throwing a die 4 times

We throw a fair 6-sided die independently four times and let $X$ denote the minimal value rolled. What is the probability that $X \ge 4$? Compute the PMF of $X$. Determine the mean and variance of $X$...
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1answer
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Two standard six sided dice are to be rolled. If the sum is an even number greater than 7, then what is the probability that both dice are even?

This question is from Mathcounts 2013- 2014, Warm Up 18, Question 253. What formula can you use to find the number of unique dice pairings? *If we have a 3 and a 4, then a 4 and a 3, the two would ...
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2answers
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Percentage Probability of Products when Multiplying 2d10

This is my first post to any Stack Exchange, so I only think I know what I'm doing. In short, my objective is to design a math game for my elementary students to practice multiplication facts (math ...
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2answers
32 views

Net gain on dice rolling

Suppose you have to pay $15 to roll a dice repeatedly until the first 6 comes up. Then you will get paid as many dollars as the square of the no of rolls (X^2). I have a equation as follows: G = Gain ...
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2answers
153 views

How many times would you have to roll a single die on average to reach a sum of at least 30?

I am primarily asking for what this kind of problem would be called. Say I have one six-sided die. How many times on average would I have to roll it in order to have a sum of at least 30? Doing some ...
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3answers
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Calculate the winning probability when using two dice with a different number of sides

I have two players with one die. The first player throws a die between 1 and 125. The second player throws a die between 1 and 350. The winner is the person who gets the higher roll. How do I ...
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1answer
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What is the probability of two people rolling a die and one person rolling higher if one of them adds 1 or 2 to their die's total?

Two players roll a 6-sided die, it is a 50/50 chance that one will roll higher, but what would the probability be if one player gets to add 1 or 2 to their die's total? I'm developing a tabletop ...
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2answers
28 views

When 2 balanced dice are rolled, what is the probability of the given numbers?

When two balanced dice are rolled, what is the probability of getting: A) a sum of equal to 7, B) a sum of exactly equal to 11, C) a sum equal to zero?
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0answers
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Combinatorics Question (Games and Dice) [closed]

A group of 10 children is given 4 different games to play. If the first two games needs 3 players each and the other two games need 2 players each, how many ways can the children be assigned to the ...
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1answer
43 views

roll 4 dice and disgard the lowest, what's the probability of the sum being over 15

I'm wondering if there is a neat way to do or set up a simulation to check my answer. I tried brute force, looking at the number of 666a rolls (21) then the number 665a rolls etc. using multinomial ...
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1answer
43 views

Probability that $N$ dice were rolled given that a five was rolled $n$ times

I know of the standard way to solve probability questions like the following: If a die is rolled 12 times, what is the probability of rolling 4 sixes? But I want to consider the reverse case: ...
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3answers
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Expected value for a sum of two special dice

I am trying to find the expected value for the sum of two dices, given that if both dices shows an identical number, then the sum is doubled. Basically if we get $1$ for a dice and $1$ for the other ...
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1answer
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Probability dice flip Central Limit Theorem problem

Suppose you flip a fair dice 300 times. Let $X$ be the number of times a $6$ was thrown. What is the probability that $X$ is greater than 60? How can I start with such a problem?
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1answer
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Dice Game: Optimal Strategy

Recently, we played a simple dice game at school. The objective of the game is to gain as many points as possible (have the largest expected value of points). Each round consists of several turns. At ...
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1answer
32 views

Can you explain this counterintuitive conditional expectation result intuitively?

Consider the following experiment. We throw a three-sided die with sides $1$, $2$ and $3$ infinitely many times. Let $T_i$ denote the outcome of the $i$'th throw. Define $N:=\min\{i:T_i\neq1\}$. Let $...
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1answer
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Simple joint probability question of two dice throw

I have a simple joint probability question I cannot understand. If I throw two dice and define the following events: $X$ - number of times 4 was obtained. $Y$ - number of even results obtained. Now ...
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1answer
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Is there a theoretical maximum number of sides a single die can have? If so what is it?

Is there a theoretical maximum number of sides a single die can have? If so, what is it? The question is fairly self-explanatory. I read the Nerdist article "This d120 is the Largest Mathematically ...
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0answers
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Sum of numbers on dice using stars and bars

I derived a general result about the sum of numbers on a die whose correctness I was wondering about, so could someone please confirm it? It is as follows: If $k$ dice are thrown, and the sum we ...
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1answer
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What is approximately the distribution of your total earning?

You play a game in a casino: you roll two dice and if the sum of the spots equals seven, you win $5$€. In every other case, you lose $1$€. You decide to play this game $120$ times. What is ...
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2answers
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Expected value. Problem with series.

We have pawn on the infinite board. We roll a dice. When we roll six we can roll dice again. We move pawn as many times as we threw dots. Pawn move's What's the expected value of pawn moves in one ...
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0answers
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What event does the probability ${{n\choose k}\over 6^n}$ describe?

The event "getting $k$ times the number $6$ in $n$ dice throws" has probability ${n\choose k}\cdot({1\over 6})^k\cdot({5\over6})^{n-k}$ So what event corresponds to ${{n\choose k}\over 6^n}$ ?
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1answer
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Question on probability with respect to dice throwing

I encountered this question while solving few practice problems on probability theory. I have solved it in my own way, but am unsure about whether it's the correct way to go about it. Four fair ...
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2answers
23 views

Bayes' Theorem Question with irregular die.

I'm having trouble with the following question: Suppose we have three, six-sided dice. These are the numbers on the sides of the dice: {1, 2, 3, 4, 5, 6} (regular die) {2, 2, 3, 4, 5, 5} (irregular ...
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3answers
54 views

Probability for rolling $n$ dice to add up to at least (a specific sum)

To clear up potential misunderstandings and make it easier to understand, I'll use this notation: Instead of writing "Rolling $n$ $m$-sided dice", I'll shorten it to "Rolling ndm". (n is the amount of ...
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1answer
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Expected value. Basic problem

We have pawn on a board and we roll dice maximally two times. When we roll six we can roll dice again. We move pawn as many times as we threw dots. What's the expected value of move on the board. Am ...
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1answer
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Combinatorics deck/dice

A player has 52 cards and dice. Every time he picks a card (without seeing it) throws the dice. How many cards at least does he have to draw to make sure that discovering them there are at least 4 ...
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1answer
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Tossing a coin (5,10) and throwing a die (1-6) at the same time twice

You flip a coin having a 5 on one side and a 10 on the other. At the same time, you throw a normal 6-sided die. So there are 12 possible combinations. You add the two numbers. This gives 10 possible ...
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1answer
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1answer
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Calculating the probability of obtaining exactly four distinct values when a die is rolled six times

Please could someone help me with determining the probability of getting $4$ distinct numbers (no order in the outcome e.g. 1,2,3,4 or 4,5,6,2 etc) or $5$ distinct from rolling a die $6$ times. So ...
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0answers
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You roll two fair dice. What is the probability to win the game based on restrictions over the sum of the results?

You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ ...
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2answers
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Choosing an integer that is most likely to be the sum of die rolls

Choose any positive integer $n$. Then roll an unbiased six-sided die as many times as needed until the sum of the results is either exactly equal to $n$ (you win) or greater than $n$ (you lose). If ...
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1answer
40 views

Determing the losing probability of a die game by rolling $n$ times under a value.

Bob is playing a dice game in which he rolls a fair dice multiple times. If he rolls $n$ times under the number $4$ (not necessarily consecutively rolls) he loses the game, and consequently, if he ...