Question

THE DATA DEPICTED BELOW IS FROM S. LTD. WHERE 300 EMPLOYEES WITH VARIOUS CATEGORIES OF PROFESSION ARE ON ROLLS.

Position Male female

Managerial 16 6

Professional 50 30

Technical 100 36

Clerical 18 44

Find the probability that:

1) A randomly selected employee is a female or a professional worker

2) A randomly selected employee is a female

3) A randomly selected employee who is found to hold a managerial position is a female

4) A randomly selected female employee having clerical position

5) A randomly selected employee given that he is a male is from technical position.

Answer 1

We have that:

1) Probability that a randomly selected employee is a female or a professional worker:

P(female OR professional)=P(female)+P(professional)–P(female AND professional)=

$=\frac{116}{300}+\frac{80}{300}-\frac{30}{300}=\frac{166}{300}=0.55$

2) Probability that a randomly selected employee is a female:

$P(female)=\frac{116}{300}=0.39$

3) Probability that a randomly selected employee who is found to hold a managerial position is a female:

$P(female|managerial)=\frac{6}{22}=0.27$

4) Probability that a randomly selected female employee having clerical position:

$P(clerical|female)=\frac{44}{116}=0.38$

5) Probability that a randomly selected employee given that he is a male is from technical position:

$P(technical|male)=\frac{100}{184}=0.54$

Answer:

1) 0.55

2) 0.39

3) 0.27

4) 0.38

5) 0.54