I would like to share a small tool I found and have been using. The program is called smallroller. It can be found at
http://www.fnordistan.com/smallroller.html.
It's not very complex so I'm not going into detailed instructions. Instead I'll tell you how I use it.
I can enter the number of dice and the required hits and know the odds.
14 dice needing 5 hits? 52% chance. 9 dice needing 2 hits? 85%.
I can work it backwards too. How many dice do I need to get better than 50% on a target of 3? 8 (not 9) is 53.18%.
If only it let me do odd on opposed tests....