Frequencies of Dice Roll Combinations and Probabilities of Dice Rolls

When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.
A. Why will some numbers come up more frequently than others?
B. Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur?
C. How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over?
D. Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined?
E. There is a very famous distribution that describes the frequency of the number of times a number comes up in a series of dice rolls, what is its name?

Solution Summary

Frequencies of Dice Roll Combinations and Probabilities of Dice Rolls are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

A popular dice game, called "craps," is played in the following manner. A player starts by rolling two dice. If the result is a 7 or 11, the player wins. If the result is 2, 3, or 12, the player loses. For any other sum appearing on the dice, the player continues to roll the dice until that outcome reoccurs (in which case th

Suppose you roll two dice
a) What are the odds in favor of rolling a sum of 10?
b) What are the odds against rolling a sum of 7 or 11?
c) In part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.
Please provide the detail of how to calculate.

Visit the following Web site Central Limit Theorem Applet and read what is posted: http://www.stat.sc.edu/~west/javahtml/CLT.html
You will choose from the pull down menu at the bottom of the page both the number of diceand the number of rolls at a time. When you "click" you will be virtually rolling your dice.
Complete t

What is the mean number of rolls of a die before a 1 is observed? Roll a die until a 1 is observed. Repeat this process 30 times and answer the following questions.
1. Obtain a point estimate of the mean number of rolls of a die before a 1 is observed.
2. The population standard deviation for the number of rolls before

There's 4 6-sided dicerolled independently. Set Y1 to be sum of the numbers on the first and second dice, Y2 to be sum of numbers on the third and fourth dice.
Convolve PMFs of Y1 & Y2 to find the probability of the outcome of the 4 rolls summing to be 8.

Problem 10)
You roll two fair dice, one red and one green.
a) What is the probability of getting a number less than 5 on both?
b) What is the probability of getting a sum of 9 on the two dice?
c) What is the probability of getting a 5 on both?