Math Probability Question involving dice

Question

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

Compute the probability of each of the following events.

Event A: The sum is greater than 9

Event B: The sum is an even number.

Answer 1

Pr(>8) = Pr(9)+P(10)+Pr(11)+Pr(12) = 4/36 + 3/36 + 2/36 + 1/36 = 10/36 = 5/18

4 ways to get 9, out of 36. 3 ways to get 10, 2 ways to get 11, 1 way to get 12

Pr(E) = 1/2 half the outcomes are even, half are odd. 18 out of 36 outcomes are even. 18/36 = 1/2

there are 6x6=36 different possible outcomes

11, 12, 13, 14,15,16

21, 22, 23, 24, 25, 26

...

61,62,63, 64,65, 66

half of them sum to an even number. 18/36 = 1/2