Question

A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?

(1) 130 of the company's employees do not have a college degree
(2) 125 of the company's employees are men

Answer 1

a) 125 < 128

b) The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)

The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)

Explanation:

Total number of employees = 255

If the probability is less than 1/2 that the employee selected will be a woman who has college degree, we have

Women with college degree < 255/2

< 128

a) if 130 of the company employee do not have college degree, we consider that all the college degree holders are women.

The women with college degree = 255 - 130

= 125

Therefore; 125 < 128 ( this is possible)

b) If 125 of the company employees are men, the number of women = 250 -125

= 130 women

The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)

The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)