What are the odds of getting the same number thrice when throwing one dice (1-6) three times?
+33661 The probability that the second throw is the same as the first is 1/6. The probability that the third throw is the same is 1/6. Therefore the overall probability that they are all the same is (1/6)*(1/6) = 1/36.
In terms of odds this is probably expressed as 35 to 1 against, since 35 in every 36 tries they won't be the same, and once in every 36 tries they will be the same.
Alan: Why is this answer different from yours, when it essentially asks the same question? If they are different questions, then how? Here is one mathematician's answer:
For three rolls, there is a 1/6 probability of rolling a six on the first
roll. There is a 5/6 probability that the first roll is not a 6. In that
case, we need to see if the second roll is a 6. The probability of the second
roll being a 6 is 1/6, giving us a probability of 11/36. There is a 25/36
probability that neither of the first two rolls was a 6. In that case, we
need to see if the third roll is a 6. The probability of the third roll being
a 6 is 1/6, giving us a probability of 1/6 + (5/6)*(1/6) + (25/36)*(1/6) =
91/216. Again, this is less than 3/6.
