8. EXTRA CREDIT: The DNA in genes can be modified with what is called an "epigenetic mark". These marks can determine whether or not a gene is expressed. Some bases in a gene lend themselves to be sites for epigenetic epigenetically marked. The gene is expressed if 0 to 5 sites are epigenetic marked, and not marks. Su ppose there is a gene which has 10 sites that can be expressed if 6 to 10 sites are epigenetically marked (a) What fraction of the possible epigenetic mark patterns (sequences of 10 marked and unmarked sites) will allow the gene to be expressed'? points (b) A mutation in the gene allows it to be expressed if up to 6 (instead of just 5) of the 10 possible sites have epigenetic marks. Now what fraction of the possible epigenetic mark patterns that the gene could have will allow the gene to be expressed? 10 points (c) Another mutation in the gene increases the possible number of sites that can have epigenetic marks to 11, but the gene is still only expressed if it has 5 or fewer epigenetic marks. Now what fraction of the possible epigenetic mark patterns t be expressed? 10 points hat the gene could have will allow the gene to