# 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.

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### Probability of three dice falling in the same quadrant of a box

This is surely really basic for most people here but it's tripping me up. You get a box and draw lines to split it up into 4 parts. I got asked what the probability was that when rolling three dice,...
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### Roll two fair dice, what is the expected value of rolls such that the sum of the two faces is the multiple of 6.

I was thinking that there were 2 cases: (1) $\\$ $X_{1}+X_{2}=6$, and the probability would be $\dfrac{5}{36}$. (2) $\\$ $X_{1}=X_{2}=6$, and the probability would be $\dfrac{1}{36}$. I am now ...
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### Probability of being able to make a given number with two out of xd6

I'm an amateur games designer, and am working on a mechanic which involves rolling on a table with numbers running from 2-12 - the full range of possibilities from adding together two six-sided dice. ...
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### Rolling dice against each other?

After doing some research, I found that the probability of rolling an n-sided die against another, equivalent die and landing a higher number on the first rolled dice to be ((n−1)/2)/n, where n is the ...
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### Probability of Rolling a $1$ on an $n$-Die in $r$ Attempts

I roll an $n$ sided die, numbered $1 \to n$. If I roll a $1$, I walk away; otherwise, I roll the die again. This process could repeat indefinitely. What is the probability, $P(n,r)$, that I will roll ...
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### 7th Sea 2e: Grouping dice results into sets of 10 vs doing the same with Tarot cards.

Note: While an interesting problem on its own, it also struck me as an excellent example of how marvelous the human brain is, as it is able to almost effortlessly negotiate a task that (at least to ...
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### Probability of obtaining a heads on the coin before a 1 or 2 on the die?

I came across this question recently and can't seem to find the correct approach. Any help would be appreciated! An experiment consists of first tossing an unbiased coin and then rolling a fair ...
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### Probability of rolling dice twice

Did I calculate the correct probability for these simple scenarios: 1: What is the probability of rolling 3 and 4 with two dice in two rolls? If you roll either 3 or 4 in the first roll, you put ...
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### If you roll four dice what is the probability of getting at least two sixes?

First of all, I know there are a lot of these and similar questions already online but I am trying to solve this on my own and I need you to tell me what I am doing wrong. So, in class we solved ...
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### Probability of $3$ doubles when two dice roled $4$ times

I thought that when rolling two dices to get only pairs is for a single roll $\frac{1}{6}$ for two $\left(\frac{1}{6}\right)^2$, and for three $\left(\frac{1}{6}\right)^3$. But since I have 4 rolls ...
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### How to statistically beat this dice game?

There is a dice game on this site where you can bet a video game's currency in games. I was wondering if any of the more statistically minded could come up with a way of beating the system? The game's ...
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### Dice throw, joint distribution.

The two dice were thrown. $X$ is random variable of the amount of 5 in throw. $Y$ is a random variable of 6 in throw. Compute $\mathrm{cov}(X,Y)$. I suppose, that for $E(X)$ and $E(Y)$ we should use ...
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### how to calculate the P(the sum of upward face after 7 dice rolls <= 30)

I'm new to the stackexchange math community so forgive me if there are problems with the question format or the question itself. I'm new to probability and is trying to learn the concept of ...
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### Do d20 dice with different number arrangements have the exact same probability for each value?

I have three d20 dice with the following number arrangements: Each pair of opposite sides add up to 21. 1 shares edges with (clockwise) 2, 5, and 8, and shares vertices with (clockwise) 2, 3, 4, 5, ...
From here: It looks like: It is supposed to say 'different from six' rather than 'different from three' $T = \inf\{m: X_{m} = X_{m+1} = X_{m+2} = 6\}$ In every triple $P(all \ 6) = 1/216$ ...