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Abstract
Motivated by a problem on the 67th William Lowell Putnam Mathematical Competition,we will summarize three different solutions found on a website. This Putman problem is aspecial case of Sylvesters four point problem! Suppose four points are taken at random ina convex body; what is the probability that they form a convex quadrilateral? We will seethat there exists a relationship among Croftons formula, random secants in two dimensionsand the solution to this question. We will then present the solution following Kingman [3]to the Sylvesters four point problem in two and three dimensions for a unit ball by lookingat convex bodies in three and four dimensions, respectively.