SOLUTION: You roll two dice. What is the probability that you will roll a combination where the difference is less than two?

Question 294546: You roll two dice. What is the probability that you will roll a combination where the difference is less than two?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Do you mean absolute value of the difference or not?
We'll do it both ways.
There are 36 possible outcomes for the roll of two die.
Here are the outcomes and the absolute value of the difference.
1 1 0
1 2 1
1 3 2
.
.
.
6 5 1
6 6 0
When you look at all of the occurences you get,
0, 6 outcomes
1, 10 outcomes
2,8 outcomes
3,6 outcomes
4,4 outcomes
5,2 outcomes
Less than two, that's the total of 0 and 1 which is 16 outcomes.
P(diff<2)=16/36=4/9.
.
.
.
If we don't use absolute value,
1 1 0
1 2 -1
1 3 -2
.
.
.
6 5 1
6 6 0
When you look at all of the occurences you get,
-5 ,1 outcomes
-4 ,2 outcomes
-3 ,3 outcomes
-2 ,4 outcomes
-1 ,5 outcomes
0 ,6 outcomes
1 ,5 outcomes
2 ,4 outcomes
3 ,3 outcomes
4 ,2 outcomes
5 ,1 outcomes
Less than 2, would be from -5 to 1, for a total of 1+2+3+4+5+6+5=26 outcomes
P(diff<2)=26/36=13/18.
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