probability and statistics

Question

1. 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.
2. Event : The sum is greater than 7 .
3. Event : The sum is not divisible by 4.

Answer 1

Event 1: What are the possibilities are 6x6 =36

no. of ways sum is greater than 7 is: 36- less than 7= 36-16=20

So Answer is 20/36 or5/9

Event 2

no. of ways sum is not divisible by 4:

36- (ways of getting divisible by 4- 4,5-3, 3-5,6-6,6-2,2-6 = 6)

36-6= 30

probability is 30/36 which is 5/6