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

>: 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 he
seems to get confused and ended up with 8 in there somewhere.

May I suggest placing coordinates on the corners of the rectangle. The
coordinate (x,y) would represent x=length of short part of 22-ft stick, y=length
of 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).

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I think this is what Gary meant. Now any point in the trapezoid to the left
has coordinates (x,y) where x<y. Area of trapezoid = 4*(4+8)/2 = 24. Area of
rectangle = 4*11 = 44, so probability is 24/44.

Gary obviously did better in geometric probability than he lets on, but he
needed a picture!

Eileen Schoaff
Buffalo State College