I have seen that the formula to calculate the number of times a given sequence of nucleotides occur in a target genome is derived from that to calculate the expected frequency of restriction sites:
a = (g/2)^G+C × ((1-g)/2)^A+T,
a = probability g = G+C content of the target genome C+G = number of G and C in the stretch A+T = number of A and T in the stretch.
An example was given for the mitochondrial genome and the restriction site for EcoRI (GAATTC). I calculated, based on the example:
a = (0.44/2)^2 × (1-0.44)^4 = 0.0005
given that the length m of the mitochndrial genome is 16 000 bp, the number of occurrences is:
n = am = 0.0005 × 16 000 = 4.92 (against 4.80 reported in the paper).
a = (0.58/2)^11 × (0.42)^14 = 1.22×10^-6 * 3.24×10^-10 = 3.95×10^-16
and the number of occurrences is:
n = 3.95×10^-16 × 16*10^6 = 6.32×10-9
Looks to me, that the primer should not occur at all in the E. coli genome.
Are the formula and its application correct? Also, I don't like the fact that one needs to know the CG content beforehand (although, one can assume 50% content) and an exponent at the 11th power; is there an alternative formula?