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Suppose two fair dice are rolled at the same time.

Which of the following events are independent?

One die is a $1$; sum of the two dice is $4$.

One die is prime; sum of the two dice is $2$.

One die is a $3$; the other die is also a $3$.

One die is a $6$; sum of the two dice is NOT a $12$.

One die is a $6$; sum of the two dice is a $12$.