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

7

.

Event

B

: The sum is not divisible by

3

and not divisible by

6

.

Write your answers as exact fractions