Assume that we break the stick at points X and Y. Assume X<Y. Then for the stick to form a triangle, the three lengths X,YX and 1Y should satisfy the following three inequalities X+(YX)>1Y(YX)+(1Y)>XX+(1Y)>YX which is nothing but the triangluar region between the points (0,0.5),(0.5,0.5) and (0.5,1) and has the area of 1/8. We should also consider the case Y<X and by symmetry, the area is same. Now, X and Y comprise of the entire square region X1 and Y1. Hence the required probability is 2×1/8=1/4.