This problem is quite interesting:

A fine needle of length l is dropped at random on a
board covered with parallel lines distance d apart where d>l as in the
figure. Find the probability that the needle intersects any of the
lines.

http://web.mit.edu/urban_or_book/www/book/chapter3/images3/fig3.17.gif

The answer is located at http://web.mit.edu/urban_or_book/www/book/chapter3/3.3.1.html