Question

Here are the projected numbers (in thousands) of earned degrees in a certain country during one academic year, classified by level and by the sex of the degree recipient:

	Bachelor's	Master's	Professional	Doctorate
Female	932	403	52	28
Male	663	270	42	28

Use these data to answer the following questions.

(a) What is the probability that a randomly chosen degree recipient is a man? (Round your answer to four decimal places.)


(b) What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man? (Round your answer to four decimal places.)


(c) Use the multiplication rule to find the probability of choosing a male bachelor's degree recipient. Check your result by finding this probability directly from the table of counts. (Round your answer to four decimal places.)

Answer 1

	Bachelor's	Master's	Professional	Doctorate	Total
Female	932	403	52	28	1415
Male	663	270	42	28	1003
Total	1595	673	94	56	2418

a) Probability that a randomly chosen degree recipient is a man

P(man) = (Total degrees earned by male)/(Total earned degrees) = 1003/2418 = 0.4148

b) What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man = P(A|B)

where A is a person having Bachelor's Degree

B That person should be a Man

P(A|B) = 663/1003 = 0.6610

c) Using Multiplicative rule choosing a male bachelors degree reciepent

= P(man)*P(bahelors degree given Male)

= (1003/2418)*(663/1003) = 0.2742

Using table of counts probability of male bachelors degree reciepent

P(Male bachelors degree reciepent) = total male bachelor degrees / total degrees

                                                    = 663/2418 = 0.2742