Consider strings of length n, n ≥ 1, over the set {a, b, c, d}. What is the correct answer to the question in Description below?

Question

Consider strings of length n, n ≥ 1, over the set {a, b, c, d}. If a string of length thirteen over {a, b, c, d} is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (Round your answer to the nearest tenth of a percent.)

Answer 1

This is 1 - the probability that each of the twelve cards following the first is not equal to the previous card = (since there are four possible selections with 3 non-matches)

1 - (3/4)^12 = 96.8%