each a positive decimal fraction.
What is the probability that
a^{2}+ b^{2}+c^{2}< 1 ?
No Solution Yet
Submitted by Ady TZIDON
Rating: 5.0000 (1 votes)
Solution 

Triples satisfying the inequality are equivalent to the points in the unit sphere. Here we want the first octant. The volume is 1/8*4/3*pi*1^3=pi/6. The space of all possible triples is just a unit cube with volume 1.
So the probability is pi/6 or about 0.52
Posted by Jer on 20210623 11:30:29 