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What are the odds for rolling a sum of 2 in a single roll of two fair dice?

The odds are 1 in 36 that you will roll a sum of 2 in a single roll of two fair dice.


Does a previous roll of the dice affect the odds what roll?

No. Each roll is independent of the previous roll (on a fair dice). The same is true for flipping a coin. Getting a six your first roll does not make you any more or less likely to roll a six the second time.


What are the odds of rolling any three pair of numbers using 6 dice?

The odds of rolling any number in one roll of one die is 1 in 1. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll is 1 in 1 times 1 in 6, or 1 in 6.Now, look at the second pair of dice. The odds of rolling any number other than a number on the first pair is 5 in 6. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll, not the pair in the first roll is 5 in 6 times 1 in 6, or 5 in 36.Now, look at the third pair of dice. The odds of rolling any number other than a number on the first two pairs is 4 in 6. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll, not one of the first two pairs is 4 in 6 times 1 in 6, or 4 in 36.To compute the total odds of rolling three pairs of numbers using 6 dice, simply multiply these odds together. That is 1 in 6 times 5 in 36 times 4 in 36, or 30 in 7776. Reducing that to lowest common fraction, you get 5 in 1296.(This calculation assumes that the three pairs are different. If two or three of the pairs are allowed to be the same, the computation is different.)


What are the odds of not rolling a 7 with a pair of 6 sided dice in 23 rolls?

About 1.5% The odds of rolling a 7 on any particular throw is 1/6. (There are six ways you can roll a seven: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), out of 36 possible outcomes.) Therefore, the odds that you don't roll a 7 on a particular roll is 5/6. The odds that you don't roll a 7 in 23 rolls is: (5/6)^23, or approximately .015=1.5%


What is th probability of rolling yahtzee on the first shake?

1/1296 (0.07716%)