SOLUTION: Suppose that two fair dice are tossed. What is the probability that the sum is an even number given that it exceeds 9

Here are all the possible 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)

Since we are given that the sum exceeds 9, we take away all those 
possible rolls whose sum does not exceed 9.  So we are left with
just these 6 rolls from the right lower corner   

 
                                     (4,6)
 
                              (5,5)  (5,6)
 
                      (6,4)   (6,5)  (6,6)

Four of those 6 have an even sum and 2 have an
odd sum.

So the desired probability is "4 out of 6" or 4/6 which reduces
to 2/3.

Edwin