algebra 2 question

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: The sum is not divisible by 4 and not divisible by5

Answer 1

The possible sums will be 2-12. 

The number of ways to arrive at each sum is

2  - 1

3  - 2

4  - 3

5  - 4

6  - 5

7  - 6

8  - 5

9  - 4

10- 3

11- 2

12- 1

Totaling the right hand column gives you 36 possible outcomes.

Removing the numbers that are divisible by 4 or 5 gives

2-1, 3-2, 6-5, 7-6, 9-4, 11-2 or 20 possible sums not divisible by 4 or 5.

The probability is given by 20/36 or 55.6%