How do you Solve for this math problem

directions: Find the odds of each outcome if a pair of number cubes are rolled.

question: a sum less then 5 or greater than 9

 Die_A  Die_B  (< 5) ?   (> 9) ?
  1    1     Yes
  1    2     Yes
  1    3     Yes
  1    4
  1    5
  1    6

  2    1     Yes
  2    2     Yes
  2    3
  2    4
  2    5
  2    6

  3    1     Yes
  3    2
  3    3
  3    4
  3    5
  3    6

  4    1
  4    2
  4    3
  4    4
  4    5
  4    6         Yes

  5    1
  5    2
  5    3
  5    4
  5    5         Yes
  5    6         Yes

  6    1
  6    2
  6    3
  6    4         Yes
  6    5         Yes
  6    6         Yes
 ──────────────────────────
           6 Y    6 Y


  P(<5) = 6 ⁄ 36 = 1 ⁄ 6

  P(>9) = 6 ⁄ 36 = 1 ⁄ 6

  P(both) = (6 + 6) ⁄ 36 = 1 ⁄ 3

Assuming that the numbered cubes are numbered 1 to 6 like a standard die and each side has an even chance of comming up:

Easiest way is just to count the different combinations.
Call one cube A and the other B.

A can be one of 6 rolls
B can also be one of 6 rolls.

This means that any possible roll is one of 36. (6*6)

Less than 5:
Neither A or B can be 4 or over (as 4 + 1 = 5 which isn't less than 5)

If A is 1 B must be 1, 2, or 3 (3 possibilites)
If A is 2 B must be 1 or 2 (2 possibilities)
If A is 3 B must be 1 (1 posibility)

6 possible rolls can make a sum less than 5

Greater than 9:
Neitehr A or B can be 3 or under (as 3 + 6 = 9 which isn't greater than 9)

If A is 6 B must be 4, 5 or 6 (3 possibilities)
If A is 5 B must be 5 or 6 (2 possibilities)
If A is 4 B must be 6 (1 posibility)

6 possible rolls can make a sum greater than 9

12 possible rolls can fulfill the given criteria.

This is 12 out of 36