Linked Questions

41
votes
7answers
18k views

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 ...
4
votes
3answers
21k 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 ...
11
votes
2answers
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? ...
14
votes
3answers
3k 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 ...
11
votes
3answers
449 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 ...
9
votes
1answer
2k 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 \...
7
votes
2answers
191 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
2answers
783 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 ...
2
votes
1answer
183 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
1answer
104 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 ...