Point P is chosen at random inside a square ABCD. What is the probability that triangle ABP has a greater area than each of triangles BCP and CDP?
P cannot fall into area ABFE, because then, any triangle DPC is greater than any triangle APB. P also cannot fall into area EID because all triangles BPC would be greater than all triangles APB.
If P falls into any of the regions IFC, ICG of IGD, all triangles APB will have greater areas than either triangles BPC or CPD. And these areas are 3/8 of the square ABCD = 37.5%.....so that's the probabilty that triangle APB will have a greater area than either BPC or CPD.
Hope this helps, whymenotsmart^m^.