13. Probability Calculus. Consider a mix of nucleotides from K different organisms. The probability of any nucleotide coming from organism is is P(Oi). For each organism, the probability of a nucleotide X is PlXIOi). The molecular weight of a specic nucleotide is given by the function FlX). a. Derive a formula for the expected value of the molecular weight of a 5 bp oligo drawn from the mix using only the terms given above. Show your work. b. Assume you draw a nucleotide X from the mix. Derive a formula for the probability that it came organism Oi using only the terms given above. Show your work