# Two dice are rolled and the values on the two uppermost faces are added together. What is the most likely outcome?

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All the possible out comes when the two dice are rolled are ( 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) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) and (6,6)

Total outcomes = 36

When we add up the values on the two uppermost faces together, then the

value of 12 comes 1 time

value of 11 comes = 2 times

value of 10 comes = 3 times

value of 9 comes = 4 times

value of 8 comes = 5 times

value of 7 comes = 6 times

value of 6 comes = 5 times

value of 5 comes = 4 times

value of 4 comes = 3 times

value of 3 comes = 2 times

value of 2 comes = 1 time

Therefore the most likely outcome = **7**

**Probability of getting sum of 7 = 6/36**** = 1/6**

When two dice are rolled and the two uppermost faces are added, the sample space is made up of 36 outcomes. This is best represented with the use of a two-way table as given in the attachments.

The sample space for rolling 1 die is {1, 2, 3, 4, 5, 6}.

At the intersection of the column and row the sum of the relevant die

outcomes are obtained , as shown in the table below.