a pair if dice is is. what that probability that the sum is equal to:
A. 5.
Here are all 36 possible ways the pair of dice can land. The
cases when their sum is equal to 5 are in 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)
So the probability that they will land such that their sum is
equal to 5 is those 4 ways out of the 36 possible rolls.
4 out of 36 is a probability of 
which reduces to 
.
---------------
B. 10.
Here again are all 36 possible ways the pair of dice can land. This
time the cases when their sum is equal to 10 are in 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)
So the probability that they will land such that their sum is
equal to 10 is those 3 ways out of the 36 possible rolls.
3 out of 36 is a probability of 
which reduces to 
.
-------------------
c. at most 9.
Here again are all 36 possible ways the pair of dice can land. This time the
cases when their sum is at most 9 are in 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)
So the probability that they will land such that their sum is
at most 9 is those 30 ways out of the 36 possible rolls.
30 out of 36 is a probability of 
which reduces to 
.
------------------------
d. at least 8.
Here once more are all 36 possible ways the pair of dice can land. This
time the cases when their sum is at least 8 are in 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)
So the probability that they will land such that their sum is
at least 8 is those 15 ways out of the 36 possible rolls.
15 out of 36 is a probability of 
which reduces to 
.
Edwin
