The "Monkey Typing Shakespeare" Problem for Compositions

Abstract

Suppose that your mother gave you n candies. You have to eat at least one candy each day. One possibility is to eat all n of them the first day. The other extreme is to make them last n days, and only eat one candy a day. Altogether, you have, famously, 2 to the power n-1 choices. If each such choice is equally likely, what is the probability that you never have three consecutive days, where in the first day you ate at least 2 candies, in the second day you ate at least 5 candies, and in the third day you ate at least 3 candies? This article describes algorithms, fully implemented in two Maple packages, to answer such important questions, and more general ones, of this kind.