probability and statistics

Question

If a pair of standard dice are rolled, what is the probability that the sum will be greater than 7

Answer 1

Let X equal the outcome. Then the question is P(X > 7). Then

P(X > 7) = 1 - P(X <= 7)

which is equal to the probability of having the outcome of one dice 1, and the other dice 6. But since we have two dices, therefore:

P(X <= 7) = 1/6 * 1/6 * 2 = 1/18.

So

P(X > 7) = 1 - 1/18 = 17/18

Answer 2

P = (number of successful outcomes) / (number of possible outcomes)

P(sum > 7) = 15 / 36