Assignment:
Employees of a company fall into four categories: Managers (4%), Administrators (12%), Technicians (26%) and Labourers (58%). If 20% of the Managers, 5% of the Administrators, 3% of the Technicians and 0.5% of the Labourers have the opportunity of promotion in the next year:
(i) What is the probability that a randomly chosen employee is a manager and will gain promotion next year?
(ii) What is the probability that a randomly chosen employee will gain promotion next year?
(iii) What is the probability that a randomly chosen employee is an Administrator if the employee has the opportunity of gaining promotion next year?
Provide complete and step by step solution for the question and show calculations and use formulas.