Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15?

Explanation

The valid sums are 15, 16, 17, and 18. Ways to get 15: (3,6,6) [3 ways], (4,5,6) [6 ways], (5,5,5) [1 way] \implies 10 ways. Ways to get 16: (4,6,6) [3 ways], (5,5,6) [3 ways] \implies 6 ways. Ways to get 17: (5,6,6) [3 ways]. Ways to get 18: (6,6,6) [1 way]. Total ways = 10+6+3+1 = 20. Probability = \frac{20}{216} = \frac{5}{54}.

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