Question

Five hundred employees were selected randomly from a few companies, and they were asked whether or not they have any retirement benefits provided by their companies. Based on the information, the following Table 2 was prepared.

Table 2

	Have Retirement Benefits
	Yes	No
Men	140	150
Women	130	80

1. If one employee is selected at random from these 500 employees, obtain the probability that the employee
   1. is a woman
   2. has retirement benefits
   3. has retirement benefits, given the employee is a man
   4. is a woman, given that she does not have retirement benefits

b)        Are the events “men” and “yes” are mutually exclusive? Why?

c)        Are the events “women” and “yes” independent? Why?

Answer 1

i. P(The employee is a woman)=(130+80)/500=0.42

ii. P(The employee has retirement benefits)=(140+130)/500=0.54

iii. P(The employee has retirement benefits| the employee is a man)=140/(140+150)=0.4828

iv. P(The employee is a women|The employee does not have retirement benefits)=80/(150+80)=0.3478

(b) P(The employee has retirement benefits and the employee is a man) =140/500=0.28 hence P(The employee has retirement benefits and the employee is a man) is not equal to zero hence  the events “men” and “yes” are not mutually exclusive.

(c) P(The employee has retirement benefits| the employee is a women)=130/(130+80)=0.6190 hence

P(The employee has retirement benefits| the employee is a women) is not equal to P(The employee has retirement benefits). Hence the events “women” and “yes” are not independent.