P = 0.5*[X + (X^3)/3]; X = sqrt(3-sqrt(2));

= 0.2190

So the probability is indeed 21.90%

There is obviously no non-calculus way of solving the problem because you need to find the area under a segment of a parabola.

]]>The experimenting, the use of mathematical tools to get a better idea of the region, utilizing powerful tools like Wolfram Alpha to do tedious calculations, and doing some good old fashioned algebra by hand were wonderful to see. The fact that you even asked questions about generalizations of this problem shows a good mathematician at work!

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