Employees of a company fall into four categories: Managers (4%), Administrators (12%), Technicians (26%) and Laborers (58%).

If 20% of the Managers, 5% of the Administrators, 3% of the Technicians and 0.5% of the Laborers have the opportunity of promotion in the next year:

(i) Construct a probability tree diagram for this data.

(ii) What is the probability that a randomly chosen manager will gain promotion next year?

(iii) What is the probability that a randomly chosen employee is a manager and will gain promotion next year?

(iv) What is the probability that a randomly chosen employee will gain promotion next year?

(v) What is the probability that a randomly chosen employee is an Administrator if the employee has the opportunity of gaining promotion next year?