International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 941920, 11 pages
Research Article

Probabilities as Values of Modular Forms and Continued Fractions

Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA

Received 12 May 2009; Accepted 26 August 2009

Academic Editor: Pentti Haukkanen

Copyright © 2009 Riad Masri and Ken Ono. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg- Gordon-Göllnitz continued fractions. One particular evaluation depends on a result from Ramanujan's famous first letter to Hardy.