Instead of thinking of this as rolling 1 die three times, think of it as rolling 3 dice once. The first die will be something. The 2nd die will have a 1/6 chance of being the same as the first. The 3rd die will have a 1 in 6 chance of being the same as the first. As for the 3rd die matching the 2nd, this gets tricky. There is a 1/6 chance it will be the same as the 2nd, but you must then adjust for the 3rd die being the same as the first and second. Having all three the same would be 1/6 * 1/6 or 1/36. So the probability would be 1/6 + 1/6 - 1/36 or 11/36
It depends upon how you are picking these numbers. Let's say you are rolling two dice. The probability of rolling 2 fours is 1 in 36. The probability of exactly 1 five is 10 in 36, while the probability of at least 1 five is 11 in 36. The probability of exactly 1 six is 10 in 36, while the probability of at least 1 six is 11 in 36. The probability of at least 1 five or 1 six is 19 in 36. The probability of exactly 1 five or six is 15 in 36. So no matter how you look at it, with dice rolling, the probability of 1 five or 1 six is bigger than the probability of 2 fours. However, if you are picking numbers from a hat, then the probabilities are different.
The probability of rolling at least one 2 when rolling a die 12 times is about 0.8878. Simply raise the probability of not rolling a 2 (5 in 6, or about 0.8333) to the 12th power, getting about 0.1122, and subtract from 1.
one fourth
The probability of rolling at least one '1' with six dice is 66.5% [1-(5/6)^6]*100%
It is 0.9459
The probability of rolling a 4 in a die is 1 in 6, or about 0.1667. The probability, then, of rolling a 4 in at least one of two dice rolls is twice that, or 2 in 6, or 0.3333. The probability of rolling a sum of 4 in two dice is 3 in 36, or 1 in 18, or about 0.05556.
The probability of NOT rolling a 3 with one die is 5/6 so the probability of NOT rolling a 3 with a roll of two dice is 25/36. The probability of rolling at least one 3 is 1–25/36=11/36, a bit less than 1/3.
With one roll of three dice, the probability is 7/8.
The probability of rolling a six is 1 out of 6, or 1/6. Now, perhaps your question is: If I roll a die 180 times, what is the probability of rolling a six at least once. This is the same as rolling a die 180 times and never once rolling a six. The probability is (5/6)180 which is 5.59 x 10-15.
11/12
There is a 1/2 chance of rolling an odd number on either die, so 1/2 X 1/2 = 1/4. 1/4 is the probability that both die will have odd numbers, so 3/4 is the probability that at least one is even.
When rolling one die, the probability of getting a 4 is 1 in 6, or 0.1667. If two dice are rolled, you get two unrelated chances of rolling at least one 4, so the probability is 2 in 6, or 0.3333.