SOLUTION: Three dice are tossed. Find the probability of rolling a sum greater than 6.

Question 1033885: Three dice are tossed. Find the probability of rolling a sum greater than 6.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
1 - Pr(sum <= 6)

Now we have to count the number of ways we can obtain a sum at most 6.

Sum of 3: (1,1,1) -- 1 way
Sum of 4: (1,1,2), (1,2,1), (2,1,1) -- 3 ways
Sum of 5: (1,1,3) (and permutations) (1,2,2) -- 3+3 = 6 ways
Sum of 6: (1,2,3), (1,1,4), (2,2,2) -- 6+3+1 = 10 ways
So Pr(sum <= 6) = (1+3+6+10)/216 = 20/216 = 5/54

Pr(sum > 6) = 1 - (5/54) = 49/54
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