Yes, you can roll one die (of a two dice set) at a time. Statistically, since they are unrelated, even if rolled together, it does not matter if you roll one or two at a time.
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You cannot roll "a dice" because it is one die, many dice. If you roll an ordinary, 6 faced die, the probability that it will land on 1 is 1/6.
The probability that you will roll doubles on a pair of dice is 1 in 6. The probability that you roll "something" on the first die is 1 in 1. The probability that the second die will match the first die is 1 in 6. The resultant probability is simply the product of (1 in 1) and (1 in 6).
It is 1/12.
With a single roll of a fair die, it is 1/6.With a single roll of a fair die, it is 1/6.With a single roll of a fair die, it is 1/6.With a single roll of a fair die, it is 1/6.
The probability of rolling a 1 on a die is 1/6 if you roll it once.