Precalc probability dice problems

I can't do these for the sake of my life!!!

Can someone please explain?



A red die and a green die have been rolled. What is the probability of the event?

1.The number on the red die is greater than the number on the green die (Answer is 5/12 but how?)
2. The sum is less than 10.
3. The sum is even.
4. The sum is prime.
5. The sum is 7 or 11.


I have a quiz tomorrow and am afraid this one will ruin my 100% spree! Plz help!!!! :-(

Thanks!!!!

1. Possible Red: 1,2,3,4,5,6 Possible Green: 1,2,3,4,5,6

Red > Green when:

Red 2, Green 1; P=(1/6)(1/6)=1/36
Red 3, Green 2, or 1; P=1/36+1/36
Red 4, Green 3,2, or 1; P=1/36+1/36+1/36
...
Red 6, Green 5,4,3,2, or 1; P=(5/36)

Total=15/36=5/12

2. Total possible sums:

2 (1,1)
3 3 (1,2 or 2,1)
4 4 4 (1,3 or 2,2 or 3,1)
5 5 5 5 (1,4 or 2,3 or 3,2 or 4,1)
6 6 6 6 6 (1,5 or 2,4 or 3,3 or 4,2 or 5,1)
7 7 7 7 7 7 (1,6 or 2,5 or 3,4 or 4,3 or 5,2 or 6,1)
8 8 8 8 8 (2,6 or 3,5 or 4,4 or 5,3 or 6,2)
9 9 9 9 (3,6 or 4,5 or 5,4 or 6,3)
10 10 10 (4,6 or 5,5 or 6,4)
11 11 (5,6 or 6,5)
12 (6,6)

36 possible sums from the different colored dice. Take all sums less than 10 = 30/36=5/6

3. Sum is even = 18/36

4. Sum is prime = 15/36

5. Sum is 7 or 11 = 8/36 = 2/9