DNA sequences are made up of 4 nucleotides A, C, G and T. In reality, they are not equally likely to arise and are not independent; however, to start let's pretend they are.

(a) Assuming that each base appears with equal frequency, what is the probability of finding the sequence ACTAGATTAC in that order?

(b) Assuming that each base appears with equal frequency, what is the probability of finding the sequence AAAAAAAAAA?

(c) The multinomial distribution gives the probability of finding x1 elements of type 1, x2 elements of type 2, ... with probabilities p1, p2,..., etc. It is a generalization of the binomial distribution where we had only two categories, where p2 = 1 p1. The multinomial distribution for N total elements with n possibilities is given by:

P(x ,x ,...,x ) = N! px1px2...pxn (1) 12 n x1!x2!...xn!12 n

Given this information, and assuming that each base appears with equal probability, what is the change of finding a sequence of length N = 10 in any order that is like the one in (a), which contains 4 A's, 3 T's, 1 G, and 2 C's?

(d) In reality, the nucleotides do not appear with equal probability. Because of base pairing, the number of A and T are nearly equal, and the number of G and C are nearly equal (Chargraff's rules). In the Human genome, the GC content makes up 40.7% of the genome.1 Given that real information, what is your revised result for (c)?