In constructing genomic libraries, the relationship between the sample size N required to achieve a probability p of sampling a desired gene present at a frequency f is given by

N = ln(1-p)/ln(1-f)

f can also be viewed as a fraction of the genome present in any fragment. If you are constructing a genomic library using 1kb fragments of a 4 Mb genome, calculate N to reach a probability of: (a) 0.95, and (b) 0.99.