```Date: Dec 4, 1996 11:59 AM
Author: Eileen Schoaff
Subject: geometric probability

>I recently used this problem from the NSML contest problem database. >I can't seem to solve it directly. Any help on it would be >appreciated! >: an 8-ft stick and a 22-ft stick are both randomly broken into>two parts. What is the probability that the longer part of the>8-ft stick is longer than the shorter part of the 22-ft stick?>I like Gary Tupper's explanation of making the rectangle 4 x 11, but then heseems to get confused and ended up with 8 in there somewhere.May I suggest placing coordinates on the corners of the rectangle.  Thecoordinate (x,y) would represent x=length of short part of 22-ft stick, y=lengthof long part of 8-ft stick.  The rectangle would have vertices at (0,4), (0,8),(11,4), and (11,8). Then draw a segment representing where these lengths would be equal, from (4,4)to (8,8).     -----------    |       /   |    |      /    |    |     /     |    |    /      |     -----------I think this is what Gary meant.  Now any point in the trapezoid to the lefthas coordinates (x,y) where x<y.  Area of trapezoid = 4*(4+8)/2 = 24.  Area ofrectangle = 4*11 = 44, so probability is 24/44.Gary obviously did better in geometric probability than he lets on, but heneeded a picture!Eileen SchoaffBuffalo State College
```