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Three random squares (Posted on 2021-06-23) Difficulty: 3 of 5
Given three random numbers a, b, and c
each a positive decimal fraction.

What is the probability that

a2+ b2+c2< 1 ?

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 3
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 2021-06-23 11:30:29
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