Question

The genderwise data of a sample of 6000 employees selected from class 3 and class 4 employees in the government jobs of a state are shown in the following table:

class of employee	gender		total
	Males	Females
Class 3	3600	900	4500
Class 4	400	1100	1500
Total	4000	2000	6000

One employee is randomly selected from all the class 3 and class 4 employees in government jobs of this state.

(1) If the selected employee is a male, find the probability that he belongs to class 3.

(2) If it is given that the selected employee belongs to class 3, find the probability that he is a male.

 

Answer 1

Suppose, A = Event that an employee belongs to class 3
B = Event that an employee belongs to class 4
C = Event that an employee is a male
D = Event that an employee is a female

∴ P(A) = \(\frac{4500}{6000}\),

P(B) = \(\frac{1500}{6000},\)

P(C) = \(\frac{4000}{6000}\)

and P(D) = \(\frac{2000}{6000}\)

(1) A|C = Event that employee selected is a male, then he belongs to class 3

P(A|C) = \(\frac{P(A∩C)}{P(C)}\)

= \(\cfrac{\frac{3600}{6000}}{\frac{4000}{6000}}\)

= \(\frac{3600}{4000}=\frac{9}{10}\)

(ii) C|A = Event that an employee selected belongs to class 3, then he is a male.

P(C|A) = \(\frac{P(A∩C)}{P(C)}\)

= \(\cfrac{\frac{3600}{6000}}{\frac{4500}{6000}}\)

= \(\frac{3600}{4500}= \frac{4}{5}\)