Training Completion Promoted Not Promoted Total
Completed 60 20 80
Not Completed 30 40 70
Total 90 60 150
3.1 Calculate the probability that a randomly selected employee:
a. Has completed the training.
b. Has been promoted.
c. Has been promoted, given that they completed the training.
3.2 Given that an employee was promoted, what is the probability that they had completed the training? Use Bayes' Theorem to solve this.
3.3 Are the events "being promoted" and "completing the training" independent? Justify your answer using appropriate probability calculations.