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 6.

Write your answers as exact fractions

--------------------------------------…
P(A) = ?
P(B) = ? -

If you roll two fair dice you should determine the number of possiblilities of obtaining each sum and then there probabilities of obtaining exactly that sum. You should have determined the following:

Sum ------Possibilities -----Probability
1 --------- impossible -------------0
2 -------------- 1 ----------------------1/36
3 -------------- 2 ----------------------2/36
4 -------------- 3 ----------------------3/36
5 -------------- 4 ----------------------4/36
6 -------------- 5 ----------------------5/36
7 -------------- 6 ----------------------6/36
8 -------------- 5 ----------------------5/36
9 -------------- 4 ----------------------4/36
10 ------------ 3 ----------------------3/36
11 ------------ 2 ----------------------2/36
12 ------------ 1 ----------------------1/36
Total -------- 36 --------------------- 1

P(A) represents:

8 -------------- 5 ----------------------5/36 or
9 -------------- 4 ----------------------4/36 or
10 ------------ 3 ----------------------3/36 or
11 ------------ 2 ----------------------2/36 or
12 ------------ 1 ----------------------1/36

or means add each of the probabilities

P(A) = 5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 15/36 = 5/12

P(B) represents not rolling 6 or 12:

NOT:
6 -------------- 5 ----------------------5/36 or
12 ------------ 1 ----------------------1/36

not means complement:

P(B) = 1 - (5/36 + 1/36) = 30/36 = 5/6

15/36
1/6