find the probability

cosinerburc · Hodge Conjecture Offline Joined: 23 Jan 2005 Posts: 87

three points are chosen from the interval [0,1].Fİnd the probability of choosing these points such that the longest distance betweeen two points is <= 1/2

**Posted:** Sun Feb 06, 2005 3:12 am

DusT

I think I have an idea Take the cube with one corner $(0,0,0)$ and another $(1,1,1)$ with side $1$ , parralel to axes. Now any point in this cube correspond to a choice of 3 points on the segment $[0,1]$ . Draw the regions for which these points are at a distace less than $\frac12$ . It is easied if you will study first the 2-D case Mr. Green

**Posted:** Sun Feb 06, 2005 7:21 am

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A step forward can sometimes be the result of a kick in the @ss. Mr. Green

cosinerburc · Hodge Conjecture Offline Joined: 23 Jan 2005 Posts: 87

sorry,but i could not understand,can u explain it in other words

**Posted:** Mon Feb 07, 2005 7:32 am

grobber

His referring to the fact that you can treat it geometrically. Represent the outcome by a point with coordinates $0\le x,y,z\le 1$ in the cube $[0,1]\times[0,1]\times[0,1]$ , where $x,y,z$ are the lengths of the segments you get.

**Posted:** Mon Feb 07, 2005 7:44 am