Suppose Bill is graduate of Slacker University, and he took a little “shortcut” when he was asked to build a software system that could take a pattern, P, of length, m, and text, T, of length, n, with both defined over the same alphabet of size d for some constant d > 1, and determine whether P is a substring of T. Namely, Bill’s software simply returns the answer “no” whenever it is asked to determine whether a pattern P of length m is contained in a text T of length n. When confronted by his Boss about this software, Bill replied that his software system is almost always correct, that is, Bill claims that his software fails with probability that is o(1) as a function of m and n. Give an asymptotic characterization of the probability that Bill’s simple algorithm incorrectly determines whether P is a substring in T, assuming that all possible pattern strings of length m are equally likely. Is Bill right about his software?