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. Calculating the probability of any given result on 2d6 (or any other number of dice, when all of them are summed) […]

I am trying to find the pmf of rolling a die until 3 consecutive 6s turn up. I am able to find the expected value using a tree diagram, but the pmf is not obvious to me. Let A be the event of not rolling 6, and let B be the event of rolling a […]

Let’s say I have a regular fair die, but instead of digits 1 through 6, there are three 0s and three 1s. I can generate a random $n$-digit binary number as follows: if initially I roll a zero (or a series of them), I ignore them; then what is left to do is just roll […]

Problem I want to create an ‘event’ with probability of $\frac{1}{7}$ with a single dice as efficiently as possible (to roll the dice as little as possible). To give you some better understanding of the question, if I would like an event with probability of $\frac{1}{9}$, I could easily do it in various ways. One […]

I am having trouble with solving the following problem: The probability that a $d$-sided dice lands on its $k$th side is equal to $p_k$ for $k\in \{k\in\mathbb{N},k≤d\}$ and $p_1+p_2+p_3+…+p_d=1$. Roll this dice (at least once) until every side is rolled equally many times. Find a function $F(p_1,p_2…)$ which gives the expected number of rolls $n$ […]

Two scenarios: 1. Using one die, roll a 6 twice. $\frac16\times\frac16=\frac1{36}$ Rolling two dice roll the same number (a pair). $\frac6{36}=\frac16$ Why are these two probabilities different? Because the events are independent, isn’t rolling a pair the same as rolling a die twice? In a sense, rolling two dice at once is the same as […]

What is the expected value of the absolute difference between 2 N faced dice? What about the difference between 2 dice one with N faces and one with M faces? While finding the expected value of 2 random variable sums or differences are simple enough, how do you deal with absolute value of differences? Thanks

I know that a Binomial Distribution, with parameters n and p, is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. I read that when the sum of the roll of two dices is a binomial distribution. Is this […]

I am having trouble understanding how you get $91/216$ as the answer to this question. say a die is rolled three times what is the probability that at least one roll is 6?

I roll a die until it comes up $6$ and add up the numbers of spots I see. For example, I roll $4,1,3,5,6$ and record the number $4+1+3+5+6=19$. Call this sum $S$. Find the standard deviation of $S$. I have been looking for an easy way to do this because I know I can use […]

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