SOLUTION: suppose two fair dice have been rolled and the sum of their top faces is divisible by 5. What is the probability that both of them have landed on 5?

We want the conditional probability that the roll is (5,5)
given that the sum is divisible by 5, that is, 5 or 10.

We can express that by:

P(two fives | sum divisible by five)

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Here are all 36 possible rolls of a pair
of dice:

(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)

We are given that the sum of their top
faces is divisible by 5, so we reduce 
the sample space to just those with
what is given, that their sum is either 
5 or 10:

                  (1,4) 

            (2,3) 
 
      (3,2) 

(4,1)                         (4,6) 

                        (5,5) 

                  (6,4) 

There are 7 in the reduced sample space.
Only one of those is (5,5).

So the desired conditional probability is 1/7.

Edwin