Answer to Question #184419 in Statistics and Probability for Sunny Paul Paulose

Question

The data for the promotion status and academic qualification regarding 100 employees of a company is as follows:

Promotional. MBA. Academic qualification. Total

Status. Non - MBA

Promoted. 12. 48. 60

Not promoted. 18. 22. 40

Total. 30. 70. 100

At random one employee is picked up. What is the probability that:

1. He is MBA

2. He is promoted

3. He is promoted given that he is an MBA, and

4. He is an MBA given that he is promoted

5. He is promoted and MBA too?

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & MBA & Academic\\ & & qualifications & Total \\ & & Non-MBA\\ \hline Promotional\\status & & \\ Promoted & 12 & 48 & 60 \\ Not\ promoted &18 & 22 & 40 \\ Total & 30 & 70 & 100 \end{array}$$

1. $P(MBA)=\dfrac{30}{100}=0.3$

2. $P(promoted)=\dfrac{60}{100}=0.6$

3. $P(promoted|MBA)=\dfrac{12}{30}=0.4$

4. $P(MBA|promoted)=\dfrac{12}{60}=0.2$

5. $P(promoted\cap MBA)=\dfrac{12}{100}=0.12$