We assume this is a fair die, not loaded.

This means each side 1-12 has an equal probability of 1/12 of being rolled.

The problem asks, P(Roll > 7)

Greater than 7 means our sample space is {8, 9, 10, 11, 12}

If each of these 5 faces have an equal probability of being rolled, then we have:

P(Roll > 7) = P(Roll = 8) + P(Roll = 9) + P(Roll = 10) + P(Roll = 11) + P(Roll = 12)

P(Roll > 7) = 1/12 + 1/12 + 1/12 + 1/12 + 1/12

P(Roll > 7) =

**5/12**