Question

In a marketing company, the probability that a randomly selected employee is a professional is 60%, while the probability that the employee has a managerial burden is 36%. Furthermore, the probability that the employee is managerial given that he is a professional is 40%.

An employee is selected at random

1) Calculate the probability that it is professional and managerial

2) Calculate the probability that he is professional, given that he is managerial.

Answer 1

A: Employee is a professional

B: Employee has a managerial burden

P(A) = 0.6

P(B) = 0.36

Probability that the employee is managerial given that he is a professional: P(B|A) = 0.4

P(B|A) = P(B∩A)/P(A)

P(B∩A)/0.6 = 0.4

P(B∩A) = P(A∩B) = 0.4*0.6 = 0.24

P(A∪B) = P(A)+P(B)-P(A∩B)

= 0.6+0.36-0.24

= 0.72

1. Probability of choosing a manager = P(B)/P(A∪B) = 0.36/0.72 = 0.5

2. Probability that he is professional, given that he is managerial = P(A|B) = P(A∩B)/P(B) = 0.24/.36 = 0.67