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.
ANSWER: 37/72
SOLUTION: Denote this probability by p, and let the three numbers that come up be x, y, and z.
We will calculate 1-p instead: 1-p is the probability that x >=(y+z); y >=(z+x), or z>=( x+y).
Since these events are mutually exclusive, 1-p is just 3 times the probability that x >=(y+z). This happens with probability (0+1+3+6+10+15)/216 = 35/216,
so the answer is (1-P)=3*35/216 =35/72.
Therefore P= 37/72.
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