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Gambler's triangulation (Posted on 2010-03-18) Difficulty: 3 of 5
I simultaneously toss three standard dice.
I get 3 numbers, 1 to 6, not necessarily distinct. Evaluate the probability that these numbers can represent sides of a triangle.

See The Solution Submitted by Ady TZIDON    
Rating: 3.5000 (2 votes)

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Solution Solution | Comment 3 of 9 |
Three standard dice will produce 63 = 216 permutations. Of these permutations, 111 are valid for sides of a triangle, therefore the probability is 111/216 = 37/72 = 0.5138.

Of the 216 permutations, there are 56 distinct combinations. Of these combinations, 34 are valid for sides of a triangle, giving a probability of 34/56 = 17/28 = 0.60714285.

Edited on March 19, 2010, 7:45 am
  Posted by Dej Mar on 2010-03-18 17:57:47

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