Four pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape. What is the probability that the rubber band is in the shape of a triangle?

in continuation to charlie's claims, which are correct, the sollution is  four times the integral in R_6 (six dimenstional space) where all variables going from zero thru 1, of the area of the triangle formed by the couples (x1,x2) (x3, x4) (x5, x6). the area of this triangle can be calculated for instance by the formula:

abs(((x3-x1)x5 + (x4-x2) x6)).

if it werent for the abs() the integral would have been easy to calculate...

 

Posted by ronen on 2005-02-12 11:31:06