SOLUTION: When two fair dice are rolled, the sum of the two dice can be any number from 2 through 12. What is the probability that this sum will be exactly a 7? Please show me how to solve

Question 72870: When two fair dice are rolled, the sum of the two dice can be any number from 2 through 12. What is the probability that this sum will be exactly a 7? Please show me how to solve this.
Found 2 solutions by jmg, stanbon:
Answer by jmg(22) (Show Source):
You can put this solution on YOUR website!
This is hard to explain on here but I will try.
If you look at all the possible combinations:
1+1=2
1+2=3
.
.
.
1+6=7
then go to the 2's, you have already used 1+ 2 so now start with
2+2=4
2+3=5
.
2+5=7
2+6=8
then go to the 3's, etc.
When you finish with all the combos, up through 6+6. You will have a total of 21 combinations that could occur when rolling two fair dice.
If you look through them you will see that there are 3 combinations that will add up to 7.
So the probability that you will roll a sum of 7 is 3/21, which reduces to 1/7

Answer by stanbon(57411) (Show Source):
You can put this solution on YOUR website!
When two dice are rolled there are 36 possible face patterns: 6*6
The patterns that give a sum of 7 are: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
So there are 7 of the 36 patterns that have a sum of 7.
Therefore the probability of getting a sum of 7 is 7/36
Cheers,
Stan H.