Consider a DNA string 6 base pairs long. Each base is a nucleic acid represented by one of the four letters A, C, T, G. Suppose the mutations at each base are independent and all four letters are equally likely at each base. Consider a random such DNA string.
(a) What is the probability that it contains at most four consecutive A's?
(b) What is the probability of ve consecutive G's?
(c) What is the probability of ve consecutive G's, given that the rst base is T or C?