Answer to Question #162655 in Statistics and Probability for Sunny

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