SOLUTION: If two fair dice are​ rolled, find the probability that the sum of the dice is 8​, given that the sum is greater than 7.

The numbers of appropriate outcomes are as follows.

     the sum of 8:  (2,6), (3,5), (4,4), (5,3), (6,2)   (5 outcomes)

     the sum of 9:  (3,6), (4,5), (5,4), (6,3)          (4 outcomes)

     the sum of 10:  (4,6), (5,5), (6,4)                (3 outcomes)

     the sum of 11:  (5,6), (6,5)                       (2 outcomes)

     the sum of 12:  (6,6)                              (1 outcome)


So, there are 5 + 4 + 3 + 2 + 1 = 15 outcomes with the sum greater than 7;

of them,  only 5 outcomes are "favorable".


Therefore, the conditional probability under the question is  P =  = .


In this problem, you can consider 15 outcomes as your space of events and 5 outcomes as the set of "favorable" events.