SOLUTION: 1. Two fair dice is rolled once. What is the probability that the sum of the outcomes equal exactly 7?

Here are all possible dice rolls with the
ones that have sum exactly 7 colored red:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Count the red ones.  There are 6 of them.
Count all of them.  There are 36 of them.

So the probability is 6 out of 36 or 6/36 
which reduces to 1/6.

Edwin