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:
EventA: The sum is greater than 6.
Event B: The sum is not divisible by 2.
Write your answers as exact fractions.

Answer 1

event a : 0/6
event b: 4/6

Answer 2

Here, Your Outcome (possibility) would be:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Now, Event which is greater than 6 is, = 21
Probability would be: 21/36 = 7/12

In short, Your Answer would be 7/12

b) Sum is not divisible by 2, = 18 possibilities
Probability would be: 18/36 = 1/2

In short, Your Answer would be 1/2

Hope this helps!