# Tagged Questions

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.

136 views

### Probability six game player [duplicate]

The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result ($x$) of rolling the die is 1 then Player 1 wins. Else the player ...
277 views

### Is rolling a dice a Gauss distribution?

I'm in an argument with a friend over rolling a dice several times, for example rolling 5 times. His argument is, that is far more difficult to roll out 1-1-1-1-1 than any other combination (for ...
69 views

### Probability of getting at least 4 numbers by rolling dice n times

I want to compute probability of getting at least 4 numbers by rolling dice n times. Now my formula is $$P = \frac{6^n - 2^n * {6 \choose 2} + 4 * 1^n * {6 \choose 1}}{6^n}$$ But by principle of ...
464 views

### Probability of rolling a 6 before an odd number [closed]

A dice is rolled many times. What's the probability of rolling a 6 before an odd number? I'm unsure of where to start with this, please help.
63 views

### Loaded die probability

The loaded die has the following probabilities: $0.3,0.2,0.1,0.1,0.2,0.1$ for $1,2,3,4,5,6$ respectively. The question asks What is the probability of rolling at least one $1$ and no $2's$ in $4$ ...
55 views

### Probability's Game

The game goes this way: There are 6 players, numered 1 to 6 (Player 1, Player 2,...,Player 6). Player 1 starts the game, he rolls a dice with six faces. If the result (x) of rolling the dice is 1 ...
112 views

### Puzzle on rolling dice game

A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6. The dealer says: "You can choose your bet on a number, any number from 1 ...
112 views

### Roll dice, high number wins.

Me and my brothers (3 of us) decided to roll a single dice to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, ...
173 views

### Proving pairwise independence and mutually independent

I have this problem that states: A = {red die is 3, 4, or 5} B = {blue die is 1 or 2} C = {sum is 7} Both the red and blue die are under equally likely probability. I need help ...
61 views

### If I do not know how much sides a dice has, how often should I throw it to know the number of sides?

Lets say we have a dice with an unknown number of sides, and we are only allowed to see the results of the rolls. How often do I have to throw the dice to know the number of sides?
1k 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 ...
86 views

### Use any dice to calculate the outcome of any probability

While looking at this question, I had a gut feeling that you can use any fair, single die with any number of sides to calculate the outcome of any probability. Assuming we express the probability as ...
585 views

### One die probability questions [closed]

I was given this exercise: If a standard die has twice the probability of rolling an odd number than an even number. Find the probability of rolling a non-prime number with this die. My attempt: ...
80 views

### Statistics dice question

$6$ people, $A, B, C, D, E, F$ sit in a circle to play a dice game. Rule of game: as you roll a die and get a number which is a multiple of $3$, give the die to the person on the ...
50 views

### two rolls of a die. independent.

for two rolls of a die, the dice fall independently. an even number shows on the first die and the event that an even number shows on the second die? this is what i got= the probability that the ...
45 views

### Probability. Fair dice with $n>6$ sides. Who wins?

I am fairly new to statistics so bear with me. Two players are playing a game with a fair dice that has $n>6$ sides. The sides are labeled $1,2,3,..,n$. The one who throws a larger number wins but ...
42 views

### Expected number of rolls until all die faces have appeared? [duplicate]

Suppose you have a die. On average, how many rolls does it take for all the faces (1 through 6) to have appeared? Also, what kind of distribution is this? (I thought of this question when watching ...
198 views

### Throwing dice 10 times

A fair dice was thrown 10 times, and it's been registered that all numbers 1-6 have appeared at least once. If this is true, what's the probability that at least 2 sixes have appeared? At first I ...
209 views

### Dice rolling game

Grallace and Womit are debating who should get to eat the last piece of Wensleydale in the fridge. To decide the issue, they agree to have a "roll-off", using the dice from their old MouseTrap set. ...
103 views

### Set of n dice are thrown…

I need help with this question: A set of n dice is thrown. All those that land on six are put aside and the others are again thrown. This is repeated until all the dice have landed on six. Let N ...
39 views

### Is the study of XdY Dice distributions well-studied and is there a simple closed form for their probability functions?

First, an explanation for those who are unfamiliar with the XdY dice format. $$XdY \sim \sum_{i=1}^X\text{Uniform}\{1, 2, ..., Y\}$$ It is the sum of $X$ discrete uniformly distributed random ...
69 views

### formula for probability of specific die outcomes

Roll some number, N, of the same kind of dice, say d6. Picking a target outcome, say 1, what is the FORMULA to determine the chance of getting 1s as a result, which is to say, how many chances of 1 ...
200 views

### Poker Dice (Combinational Probability)

I've seen similar questions to this asked, and have searched the internet. I haven't found the exact questions here and the internet doesn't have the correct answers. Play poker using 5 fair dice ...
72 views

### Probability of no 6 or no 5 when dice is rolled n times

Can anyone guide me in the general direction of the answer to the following: A die is rolled $n$ times $$A = \text{no 6s}$$ $$B = \text{no 5s}$$ $$P(A\cup B) = \;?$$ I am first finding $P(A)$ ...
26 views

### Goodness-of-Fit tests for Multinomial and Binomial Data

A box has 4000 red, 5000 blue and 1000 orange balls. A selection of 70 balls is made, with 25 reds, 35 blues, and 10 oranges being observed. Can one essentially prove that the selection was NOT a ...
183 views

### dice probability - same 2 dice in 6 dice rolls

I have this simple probability problem that I am not sure I solved correctly. I am not interested in formulas, but rather the thought process of how to solve it. Suppose we roll six 6-sided dice that ...
51 views

### What is wrong with this logic based on a geometric distribution?

Problem #10 from A Collection of Dice Problems by Matthew M. Conroy, is: Suppose we can roll a $6$-sided die up to $n$ times. At any point we can stop and that roll becomes our score. The goal is ...
63 views

### Difficult probability with dice

I am completely stuck on this probability question involving dice. Any hints or help in the right direction would be great. You are given $6$ numbers: $2, 3, 4, 7, 8, 5: n_1, n_2,\dots , n_6$. ...
82 views

### Simulate sum of N dice throws

For starters let me apologise if it isn't proper forum or if it was asked, I'm not very good at probability and what more I'm not familiar with proper english terms, so I could miss something. I'm ...
111 views

### Probability rolling two different sided die and sum being a number

I'm building an app (for those curious, for DnD) and I came across an issue with some math I did. I need to know the probability of rolling a certain number when there are two or more different sided ...
62 views

### How do I go about solving this probability question?

I was playing around with dice this morning and flipping them, when a problem suddenly hit me. If I roll $n$ normal six-sided dice, and flip every single dice, what is the probability that the ...
108 views

### 100-sided dice was rolled 98 times, how do you choose next numbes to bet, based on current outcomes.

100-sided dice was rolled 98 times, Numbers form 1 to 50 were rolled exactly once, except number 25, which wasn't rolled yet. Number 75 was rolled 49 times You can only bet if the next roll result ...
50 views

### How can I convert [number of expected success per try] into [probability of succeeding N times without failing]?

There's a push-your-luck dice game called Can't Stop where you roll four six-sided dice, group the dice into pairs of your choice, then advance tokens along paths corresponding to the sums of your ...
73 views

### conditional probability of coming up 3 at least in one dice

Sorry for the simple problem, but I wanted to make sure that my idea is right (this is is the problem 1.8.50 from Rice's book) Two dices are rolled and the sum of the face values is six. What is the ...
61 views

### Probability Dice and Expected Value

You are rolling a fair 30-sided die. (a) What is the expected number of rolls required to get a 27? (b) What is the expected number of rolls required to get a 27, followed later by a 28? For example, ...
108 views

### Probability of Sequential events on a die roll

If a person were to roll two dice and have to get a 9 or below for success. But if you fail the first time, you have the opportunity to roll it one more time for success, what is the probability of ...
30 views

### Having a value, calculating the probability of the number of times a die has been rolled

If I enter a friend's house and he has rolled a dice (d6) on a table which has a value $1$, he asks me the following, "Do you think I rolled this dice once and got $1$ or do you think I rolled it ...
147 views

### Can we simulate a biased coin with fair die? [closed]

Given a fair 6-sided die, how can we simulate a biased coin with P(H)= 1/$\pi$ and P(T) = 1 - 1/$\pi$ ?
101 views

### Monopoly dice probabilities, including doubles

According to Monopoly, when you roll a set of doubles, you get to roll again. So if we get 6;6, 5;5, 4;4, 3;3, 2;2, 1;1, we will roll again. However, Monopoly has the "speeding" rule, this means that ...
93 views

### Dice Probability (increasing numbers)

If I have 6 regular dice, (each numbered 1-6): What is the probability that when rolled that each will be a different number.(each individual di is a different number from 1-6, but a random order) ...
29 views

### Given Nd6, what is the probability that the two highest are minimum 4?

So, my statistics knowledge is rather poor, so I would welcome a formula explanation to the question: given Nd6 (6-sided dice) what is the probability that the two highest numbers are at least a 4? ...
169 views

### Probability of a rolling a dice $n$ times with $k$ faces

I need help calculating the probability of rolling $n$ dice with $k$ faces. So you have multiple dice, all with $k$ faces (number of sides on a dice) and you want to calculate the probability of a ...
70 views

### Uniform distribution on $\{1,\dots,7\}$ from rolling a die [duplicate]

This was a job interview question someone asked about on Reddit. (Link) How can you generate a uniform distribution on $\{1,\dots,7\}$ using a fair die? Presumably, you are to do this by combining ...
68 views

### probablity question related to 2 die and the classic monopoly game.

While playing monopoly I accidentally figured out that probability for landing on Illionis Avenue is most in the whole game and for landing on orange colored group ...
147 views

### Dice Game: Probability of rolling three 6's before my opponent

Let's say I'm playing a dice game with a friend. We each get two dice, and we roll all of our dice at the same time. You get one point for each 6 you have. First to score at least three points wins. ...
104 views

### Roll a dice, probability that game goes beyond one round

There are two people $A$ and $B$. Person $A$ has $8$ chips, and person $B$ has $6$ chips. Each round, both people roll a die then take that number of chips from the other person. The game ends when ...
138 views

### The average outcome of the sum of a pair of dice and the higher sum of two pairs

I'm helping my son to design a game using dice. He wants to figure out the expected outcome of the sum of a pair of $6$-sided dice, if $2$ pairs of dice are thrown and the higher pair is kept. I get ...
25 views

### Expected number of rolls to roll every number [duplicate]

If I am rolling I die until I roll every number at least once, what is the expected value of times that I will need to roll the die? After a brief computer simulation, I got 15. But why is this the ...
### Two identical dice are thrown simultaneously. Find probability of getting a $3$ and a $2$.
Two identical dice are thrown simultaneously. Find the probability of getting a $3$ on one of the dice while a $2$ on the other. I'm pretty sure the answer is $\frac{2}{36}$ but my friend says ...