Ask Dr. Math

Rolling Dice

Rolling Dice, a selection of answers from the Dr. Math archives.

Probability of Rolling a 6 on One Die

The following questions came up during a game of Risk...

Probability: 8-sided die

I have an octahedron. What's the probability I'll roll a seven?

Rolling One Die Twice

If one die is rolled twice, what is the probability of getting a 10?

Probabilities when Rolling 10 Dice

What are the odds of a player rolling the same numbers in the same order as the house on 10 dice? ...of rolling the same numbers without regard to the order in which they were rolled?

Probability of Two Dice Summing to 5

If a person rolls two dice, what is the probability of getting a five as the sum?

Sum of Two Dice

Find the probabilities of rolling different sums.

Throwing Dice More Than Once

If I throw one die once the probability of getting any one of the six numbers is 1/6. Does this change if I throw more than once?

Dice: Full House

What is the probability of rolling a full house with 5 six-sided dice?

Probability and the 'Ways Method'

Suppose we roll one six-sided die. What are the possible outcomes? What is the probabiliy of rolling a 4? If we have two dice how many outcomes are there? With two dice what is the probability of rolling a 5?

Probability of an Even Number of 6's

A fair die is thrown n times. Show that the probability that there is an even number of sixes is 1/2 * [1+(2/3)^n].

Probability in a Dice Game

How can I find the probability of each player winning, and the most likely length of the game, for a dice game that may continue forever?

What is a Biased Die?

How do we find the probability when the dice are biased?

Biased Dice

Assigning and adding probabilities.

Getting One of Each Number (1-6) Rolling N Dice

I've been trying to determine various probabilities involving randomly distributing items to a group of six people...

Die Roll Probabilities in Gaming

Players fight battles by rolling two dice and adding modifiers according to each player's advantages. Generate a chart giving the odds of victory based on modifiers.

Rolling 3 Pairs with 6 Dice

Upon playing the game '10,000' on the computer I was struck by the frequency with which 3 pairs came up...

Three Fair Dice

Find the probabilities of a total of 9 and a total of 10 when three fair dice are tossed once... Compare.

Sum of 5 or 7: Dice Probability

A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 will occur first.

Tossing a Coin and Rolling a Die

If you toss a coin and roll a die, what is the probability of obtaining: a) heads and a five b) heads or a five c) tails or a two?

Rolling a Die 600 and 5000 Times

Toss a die 600 times, 5000 times. How many times does each number come up? Approximately how many would you expect?