Question

In a large corporation, 80% of the employees are men and 20% are women. The highest levels of education obtained by the employees are graduate training for 10% of men, undergraduate trading for 30% of men, and high school training for 60% of the men. The highest levels of education obtained by the employees are graduate training for 15% of women, undergraduate training for 40% of women, and high school training for 45% of the women.
(a) What is the probability that a random chosen employee will be a
man with only a high school degree? [2]
(b) What is the probability that a random chosen employee will
have graduate training? [2]
(c) What is the probability that a random chosen employee who has graduate training
is a man? [2]
(d) Are gender and level of education of employees in this corporation
statistically independent? [2]
(e) What is the probability that a randomly chosen employee has not
had graduate training? [2]

Answer 1

Ans:

	graduate	undergraduate	high school	Total
men	0.08	0.24	0.48	0.8
women	0.03	0.08	0.09	0.2
Total	0.11	0.32	0.57	1

a)

probability that a random chosen employee will
have graduate training=0.6*0.8=0.48

b)

probability that a random chosen employee will have graduate training=0.1*0.8+0.15*0.2=0.11

c)probability that a random chosen employee who has graduate training s a man=0.1*0.8=0.08

d)

P(men and graduate)=0.08

P(men)=0.8

P(graduate)=0.11

P(men)*P(graduate)=0.8*0.11=0.088

As, P(men)*P(graduate) is not equal to P(men and graduate),so not independent.

e)

probability that a randomly chosen employee has not had graduate training=1-0.11=0.89