The Wikipedia article on the Bertrand paradox has more interesting information and pictures. The is also a Wolfram demonstration project called the Random chord paradox that you can play with.

Examples sheet 4, #2 is this classic question: "

Examples sheet 4, #2 is this classic question: "

*A stick is broken in two places, independently uniformly distributed along its length. What is the**probability that the three pieces will make a triangle*?" For a more a more complicated geometric probability problem see the blog posting on Planet Zog problems.