Suppose 20 % of the employees of company ABC have only a high school diploma, 60 % have bachelor degrees, and 20 % have graduate degrees Of those with only a high school diploma, 15 % hold management positions; whereas, of those having bachelor degrees, 30 % hold management positions.

Finally, 60 % of the employees who have graduate degrees hold management positions.

(a) What percentage of employees holds management positions?

(b) Given that a person holds a management position, what is the probability that she/he has a graduate degree?