1
vote
0answers
38 views

Can a biased physical random source be post-processed to control the bias?

Let $X_i$ with $i\in\mathbb N$ be a sequence of independent 6-ary random variables with distribution $\operatorname{Pr}(X_i=e)=p^e_i$ where $e\in\{1,2,3,4,5,6\}$ and $\sum_{e=1}^6p^e_i=1$. Let's ...
0
votes
2answers
37 views

Probability of 3 dices

Been looking through past exam papers and came across this question: Three fair dices are rolled. The probability that all three dices show 5 is 1/216. Is this true?
5
votes
2answers
96 views

Number of dice rolls taken to reach a certain sum

I was reading about sums of dice rolls and Chernoff bounds, and I thought of a question I couldn't obviously answer with the techniques I know. You're given some number $x$ and told it was generated ...
0
votes
3answers
112 views

How can I linearly decrease chance?

Suppose there are 10 different people, each holding 1 lottery ticket, and I give each of them 10% chance of becoming the 'winner'. Now let's say one of those 10 people (I dont know which one) ...
0
votes
2answers
76 views

Dice sum probability

Simulate two separate dice (use random numbers with the appropriate range) being rolled 10 times. What are the percentage of rolls that resulted in a sum of 7, a sum of 2 and a sum of 11. I came ...
1
vote
1answer
117 views

Probability of A given B & C?

I would like to sum the probability that given 3 (potentially biased) die rolls, all 3 rolls will be different-- what is the correct way to do this? So far, I have: $$ 1 - ...
2
votes
2answers
852 views

Expected sum if a fair die is rolled continuously

The problem statement is : What sum can I expect in rolling a fair die n times? How to determine the mean in a convenient way? Consider the fair die is 6 sided
3
votes
3answers
141 views

Calculating mean after removing smallest items

I'm having a tough time wrapping my head around this question. Lets say that I am doing an experiment where I roll 10 dice. Each time I roll the dice, I record the average value and repeat the ...
3
votes
2answers
274 views

The Odds of A Dice Game Ending

A fair dice roll: On a 6 you win €1 on everything else you lose €1. The game continues until you profit €500. What are the odds of the game ever ending? Update: While initially I hadn't clarified ...
3
votes
1answer
155 views

The probability of obtaining at least one roll of x from k dice each with a different number of faces

Assume you have k dice, each with some random number of sides, 1...n. I'm trying to figure out, after rolling all k dice, what is the probability of obtaining at least one roll with a given value x - ...
4
votes
1answer
539 views

Magical Loaded Dice and expected values

Let's say we have a magical biased die that allows us to set the probability of every side to whatever we want (nonzero and add up to 1, of course). And let's say this die enforces the condition that ...
7
votes
3answers
527 views

Thought experiment for dice game

Two players in a dice game to see who can roll a total of 60 first, taking turns each rolling 2 dice. For one player, one die is 4 sided and one is 6 sided. Therefore the average roll for this ...