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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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

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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

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

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.

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