Calculating Probabilities with Dice Throws

In summary, the conversation discusses the probability of getting a certain number of dice with the same value in a game where there are 5 players with 5 dice each, resulting in 25 throws per game. The probability can be calculated using the binomial theorem and the multinomial distribution formula. The conversation also touches on determining the most likely number of dice with the same value, which requires calculating all probabilities for each number.
  • #1
Lobotomy
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There is 5 players with 5 dices each = 25 throws per game

Whats the probability that there is X dices with the value Y(1-6) on the table.
for example. probability for 8 three's

this is calculated through the binomial theorem right?
http://en.wikipedia.org/wiki/Binomial_theorem
where n=25, k=8 och p=1/6calculating the probability of having X dices with the same value could be calculated with the above times six right?

so far so good.

now it gets a bit more complicated.

how to calculate:
how many dices of the same value is the most probable result? (assuming all 25 dices has been thrown)
Also, conditional probability:
i know that i have got Z dices with the same value (1-6 it doesn't matter which value). What is now the most probable result of the number of dices with the same value on the table?(i know my own result, but i don't know the 4 other players result)for instance: i get 4 three's. what is the most likely number of three's on the table totally of the 25dices?please refer to probability theory and distributions if you know them.
 
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  • #2
First "dices" is the third person singular present tense of a verb, what you do to vegetables; it is not the plural of the noun "dice". "dice" is itself the plural of the noun "die". I say this not as a criticism but because many people here do not have English as a first language- and it is a complicated language!

The binomial distribution you describe would be the probability of getting "x" dice to be a specific number. The probability of getting "x" dice the same (but any number between 1 and 6) would be a "multinomial" distribution because you might get, say "x" dice equal to 5, "y" dice equal to 3, etc.

The other way, determining the "most likely" number of dice that are the same (and again, there might be "x" dice that are equal to one number, "y" dice that are equal to another, etc.) requires calculating all the probability of each such number and seeing which is the largest.
 
  • #3
haha thank you I did not know that about dices. English is not my first language.

anyway the multinomial formula being

(n!/(x1!...xk!))*p^x1...p^xk

in the above case:
how many dices of the same value is the most probable result? (assuming all 25 dices has been thrown)n=25 p=1/6
but what exactely is x1 to xk?
 

What is the probability of rolling a specific number on a single die?

The probability of rolling a specific number on a single die is 1/6, or approximately 16.67%. This is because there are 6 possible outcomes (1, 2, 3, 4, 5, or 6) and each outcome has an equal chance of occurring.

What is the probability of rolling a certain sum with two dice?

The probability of rolling a certain sum with two dice can be calculated by dividing the number of possible ways to roll that sum by the total number of outcomes. For example, the probability of rolling a sum of 7 is 6/36, or 1/6, because there are 6 ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, or 6+1) out of a total of 36 possible outcomes.

How can the probability of rolling a certain sum with multiple dice be calculated?

The probability of rolling a certain sum with multiple dice can be calculated by using the following formula: P(sum) = (number of ways to roll the sum) / (total number of outcomes). For example, the probability of rolling a sum of 9 with three dice is 25/216, or approximately 11.57%, because there are 25 ways to roll a sum of 9 (1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3, 1+2+6, 1+5+3, 2+1+6, 2+4+3, 3+2+4, 4+1+4, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3, 1+2+6, 1+5+3, 2+1+6, 2+4+3, 3+2+4, 4+1+4, 1+3+5, and 2+2+5) out of a total of 216 possible outcomes.

How can the probability of rolling a certain sum with a specific type of die be calculated?

The probability of rolling a certain sum with a specific type of die can be calculated by using the following formula: P(sum) = (number of ways to roll the sum) / (total number of outcomes). For example, the probability of rolling a sum of 8 with a 10-sided die is 1/10, or 10%, because there is only 1 way to roll an 8 (8) out of a total of 10 possible outcomes (1, 2, 3, 4, 5, 6, 7, 8, 9, or 10).

How can the probability of rolling a certain sum with a combination of different types of dice be calculated?

The probability of rolling a certain sum with a combination of different types of dice can be calculated by using the following formula: P(sum) = (number of ways to roll the sum) / (total number of outcomes). For example, the probability of rolling a sum of 10 with a 6-sided die and a 12-sided die is 5/72, or approximately 6.94%, because there are 5 ways to roll a sum of 10 (4+6, 5+5, 6+4, 7+3, or 8+2) out of a total of 72 possible outcomes (6 possible outcomes for the 6-sided die multiplied by 12 possible outcomes for the 12-sided die).

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