SOLUTION: Two dice are rolled. Find the probability of rolling a sum greater than 6. Show your work in determining the answer.

The full space of events is the set of all pairs  (i,j), where i and j are integer numbers from 1 to 6, inclusively.

This space consists of  6*6 = 36 elements, and each element/event has the probability of  .


Of them, the outcomes where the sum is greater than 6, are


    sum  7 :  (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)     In all, 6 pairs.

    sum  8 :  (2,6), (3,5), (4,4), (5,3), (6,2)            In all, 5 pairs.

    sum  9 :  (3,6), (4,5), (5,4), (6,3)                   In all, 4 pairs.

    sum 10 :  (4,6), (5,5), (6,4)                          In all, 3 pairs.

    sum 11 :  (5,6), (6,5)                                 In all, 2 pairs.

    sum 12 :  (6,6)                                        Only    1 pair.


Thus the number of events where the sum is greater than 6 is  6 + 5 + 4 + 3 + 2 + 1 = 21.


Therefore, the probability under the question is   = .    ANSWER