I found an interesting problem that has a cool interactive applet to explore the probabilities.
It's a bit complicated and it involves a fair amount of reading.
Try it.
Even if you don't solve the problem, I think you might enjoy experimenting with the applet.
If the applet does not work on your chrome browser, try it on Safari - that's where mine worked...
If you do come up with an idea or a solution, click the assignment button and tell me.