In my country we have \$0.10, \$0.20, \$0.50, \$1, and \$2 coins. If I were to pour a bag of coins out on the table what would be the probability that I could buy a heap of \$1 snacks without needing any change? Does this change if the bag doesn't contain any whole dollar value coins?
I'm fairly sure the that $P=0.1$ for very large values of $N$ (as there is 10 possible cent values). I'd like to be able to prove this and be able to see how the probability changes with $N$, but I cant figure out a rule for the entire series & larger values of $N$.
I've written a little Python simulation to test $N$ values $0$ through $50$ and I'll edit with the results of that when it finishes.
EDIT: Results of my script seem to confirm my thought: http://pastebin.com/cD8PeuwT