Sunday, March 30, 2014

The Random Chord Probability Problem

   I am still playing with geometric probability. This Scratch project looks at an experimental (Monte Carlo) method for determining the probability that the chord of a circle, picked at random, is longer than the radius of the circle.    
   The real purpose of this project is to set the stage for using three additional Scratch programs to explore the Joseph Bertrand Paradox. His paradox indicates that how you select the random chord in a similar circle problem is important and in fact, leads to three different answers!
   This video shows the result of running the experiment.

 
   Repeated runs of the program indicate that the theoretical probability is two-thirds.
   The Scratch project can be viewed and downloaded by clicking on the following link.

  Detailed descriptions (PDF format) of the code and theoretical solution to the problem can be had by sending an email request to grandadscience@gmail.com