# Linked Questions

7answers
19k 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 ...
3answers
4k 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 ...
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? ...
3answers
537 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 ...
1answer
4k views

3answers
22k 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 ...
2answers
806 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 ...
1answer
224 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 ...
1answer
117 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 ...
0answers
24 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 ...