Quincunx or Galton’s Board

 

This activity is appropriate for an introductory probability and statistics or mathematics for elementary and middle school teachers.

 

Objectives: To motivate a study of probability and empirical probabilities.  The Galton’s Boards are useful for discussing tree diagrams and using them for computing probabilities.

 

Introduction: The Galton’s Board resembles a Pascal’s triangle.  The balls are dropped through a triangular array of nails and accumulate in the slots beneath the triangle.  The slots can be labeled with prizes and Expected Values can be computed.

 

Go to the following web sites and work trough corresponding applets and answer the questions.

http://www.users.on.net/zhcchz/java/quincunx/quincunx.1.html
http://www.qualitytng.com/Quincunx.htm
http://www.tld.jcu.edu.au/hist/stats/galton/galton16.htm
http://www.jcu.edu/math/isep/Quincunx/Quincunx.html
http://www.stattucino.com/berrie/dsl/Galton.html
http://www.rand.org/methodology/stat/applets/clt.html
http://members.fortunecity.com/jonhays/quincunx.htm

 

 

 

1. Write a brief history of Quincunx and how it works.
2. Investigate the distribution of the balls accumulated in the slots. 
3. Compute the probability of landing in each slot for a five row Quincunx.  A 5 row Quincunx has 1 nail on the top and 5 in the bottom.
4.  Label the slots of a 5 row Quincunx form left to right as: $50, $10, $10, $50 awards and compute the expected win.
5. How would you label the slots in order to minimize the expected gain with a total of $120 awards?