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1/6. With two dice there are 36 possible outcomes six of which are doubles 6/36= 1/6.
6 Of course - assuming a cube die. There are other dice available (for playing D&D) which can have for example 4 (tetrahedral dice) or 20 (icosahedral dice) outcomes.
There are 6 outcomes with one roll and 6^2 with two and 6^3 with three. So the answer is 216.
you will land on 1 or 6 5/6 times
1-(5/6)^60 ≈ 99.99822529882%