Three points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A triangle is drawn with the three random points as the vertices. What is the probability that the center of the square is inside the triangle?

(In reply to re: Faster, simpler, better by ed bottemiller)

hi ed,

it's vital to have good hunches to serve as guidelines for where to invest work.

was your notion about the "average" inscribed triangle would have area one quarter that of the framework square such an insight? im not sure. my guess is that finding the average area of a triangle inside a unit square (or, more simply, inside a unit circle) is a different problem, and may well result in something other than 1/4. certainly the average for the unit circle case is less than the average for the unit square case, unlike the situation with this problem, where we've seen the results to be identical.

Posted by FrankM on 2008-03-17 21:47:34