Here are all 36 dice rolls:
 
(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) 

The ones colored red have sum 8 or more.

Count them.  There are 15 of them.  So the 
probability that you want is 15 times out
of 36, which is the fraction 15/36 which
reduces to 5/12.

That means that five times out of twelve you can expect
to roll a sum of 8 or higher.  That is almost 42% of the
time.

Edwin