You are planning an accelerated evolution experiment with a
mutation rate of 10^-2 mutations per base pair per generation
(cells double once per generation) in which a gene requires 5
specific, individual DNA mutations for its protein product to
acquire a particular desired change of function.

(a) What is the expected proportion of the population that will
have acquired all 5 desired mutations after 20 generations?

(b) If the gene has 1005 nucleotides, what is the average number
of additional DNA mutations beyond the desired 5 that will have
accumulated?