The human genome is composed of four DNA nucleotides: A,T,G and C. Some regions of human genome are extremely G-C rich. Other regions are relatively A-T rich. Suppose that you want to compare nucleotide sequences from two regions of genome. Sixty percent of the nucleotides in the first region are G-C (30% each of guanine and cytosine) and 40% are A-T (20% each of adenine and thymine). The second region has 25% of each of the four nucleotides.
a. If you choose a single nucleotide at random from each of the two regions, what is the probability that they are the same nucleotide?
b. Assume that nucleotides over a single strand of DNA occur independently within regions and that you randomly sample a three nucleotide sequence from each of the two regions. What is the chance that these two triplets are the same?