The probability of rolling doubles with two dice is 1 in 6, or about 0.167.
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The probability of rolling a sum of 8 and doubles when rolling two dice is 1 in 36, or about 0.02778. Simply note that there are 36 permutations of two dice, of which exactly one of them (a 4 and a 4) matches the conditions specified.
The probability is 11/36.
The probability is 1.
The probability of rolling two prime numbers on a standard pair of dice is 1 in 4, or 0.25. Take the probability of rolling a prime on one die, 3 in 6, or 1 in 2, or 0.5, and square it.
The probability of rolling 7 once with two dice is 1 in 6, o 0.1667. The probability, then, of doing that twice in a row is 1 in 36, or 0.02778.