The probability that when you roll three dice you will get exactly one six is; P(one 6) = 3C1∙(1/6)∙(5/6)2= 0.347222... ~ 34.7%
where 3C1= 3!/[1!∙(3-2)!] = 3, are the three ways the six can come out, that
is the six can come out from die one, die two or die three.
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The odds of rolling any specific number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling the same specific number using six dice in one roll is 1 in 6 to the 6th, or 1 in 46,656.
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.)
The expected value if you roll a die three times is 3.5.
on a 6-sided die theres a 1/6 chance
The probability of rolling a 1 on a die is 1/6 if you roll it once.