Linked Questions
43
votes
7
answers
21k
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How often do you have to roll a 6-sided die to obtain every number at least once?
I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins.
I won, eventually, and the others finished 1-2 turns later. Now I'm ...
17
votes
4
answers
6k
views
Formula for dropping dice (non-brute force)
First of all I'm not sure where this question should be posted. I'm asking if a statistics problem is NP-Complete and if not to solve it programmatically. I'm posting it here because the statistics ...
15
votes
1
answer
8k
views
Expectation of a function of a random variable from CDF
Is it possible to calculate the expectation of a function of a random variable with only the the r.v.'s CDF? Say I have a function $g(x)$ that has the property $\int_{-\infty}^{\infty}g(x)dx \leq \...
11
votes
2
answers
2k
views
Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded?
Here is the question:
You roll a fair 6-sided dice iteratively until the sum of the dice rolls is greater than or equal to M. What is the mean and standard deviation of the sum minus M when M=300?
...
11
votes
3
answers
730
views
Die 100 rolls no face appearing more than 20 times
I am trying to wrap my head around this problem.
A die is rolled 100 times. What is the probability of no face being appearing more than 20 times? My first thought was using the Binomial distribution ...
7
votes
2
answers
1k
views
What is the probability that a student gets a better score than another on a test with randomly selected questions?
Suppose there is a set $S$ of $100$ questions and there are $2$ students $a$ and $b$.
Let $P_{ai}$ be the probability that $a$ answers the question $i$ correctly, and $P_{bi}$ the same for $b$.
All $...
4
votes
3
answers
26k
views
Odds of rolling doubles or triples given N 6-sided dice
Over the holidays I played a dice game where each player had 3 to 7 d6 to roll each turn. The game gave certain advantages to doubles and triples. I wanted to know the odds of rolling doubles or ...
4
votes
2
answers
954
views
Probability of drawing all balls in a non-uniformly distributed population
I am wondering if there is a way of calculating the following:
I have a bag with 5 balls numbered from 1 through 5 that are going to be drawn.
Due to different weights, the balls have different ...
3
votes
1
answer
357
views
Inverse Sampling according to Haldane (1945)
According to the inverse-sampling method (Haldane 1945) you continue sampling until m of the rare items have been found.
Let p be the frequency of the rare item ...
3
votes
1
answer
145
views
Combination/permutations question where repetition is allowed
So I guess this is a combination/permutations question where repetition is allowed.
What is the % chance that six six-sided dice will show at least 3 duplicates of the same number or that there will ...
3
votes
0
answers
98
views
Mean number of throws to exceed a threshold [duplicate]
Say that you have a die with n faces, and you need to throw the die until the sum of your results exceeds a given threshold.
What is the average number of throws needed?
I think that to compute that ...