Records of a company show that $12\%$ of the employees have only a high school diploma; $63\%$ have bachelor degrees; and $25\%$ have graduate degrees. Of those with only a high school diploma, $25\%$ hold management positions; whereas, of those having bachelor degrees, $44\%$ hold management positions. Finally, $80\%$ of the employees who have graduate degrees hold management positions.

a$.$ Create a tree diagram representing the above situation.

b$.$ What percentage of employees hold management positions?

c$.$ Given that a person holds a management position, what is the probability that she$/$he has a graduate degree?